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Flexibility (Fin)

Peter Hästö's Publications

Unpublished, 2000, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, Submitted, To appear, Books

Click on the Get preprint-symbol to retrieve a preprint of the publication and the Get preprint to access it on ArXiv. Some articles are available in open accesss (open access). More info at my author page at MathSciNet and my Google scholar citation count. You can also find me on the list of most cited mathematicians under the year 2003.

Books

To appear

  1. Which One Is the "Best"? A Cross-national Comparative Study of Students&Strategy Evaluation in Equation Solving, Int. J. Sci. Math. Education, to appear (R. Jiang, J. Star, L. Li, R.-D. Liu, D. Tuomela, N. Joglar Prieto, R. Palkki, M. Abánades and J. Pejlare). Get preprint Dataset
  2. Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure, Arch. Ration. Mech. Anal., to appear (with J. Ok). (open access) Get preprint

Submitted

  1. Minimizers of abstract generalized Orlicz-bounded variation energy, submitted (with M. Eleuteri and P. Harjulehto). Get preprint
  2. A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces, submitted. Get preprint
  3. Procedural flexibility in early university mathematics, submitted (with A.-M. Ernvall-Hytönen, H. Krzywacki and S. Parikka). Get preprint
  4. Riesz spaces with generalized Orlicz growth, submitted (with J. Juusti and H. Rafeiro). Get preprint
  5. Bloch estimates in non-doubling generalized Orlicz spaces, submitted (with P. Harjulehto and J. Juusti). Get preprint

2022

  1. Maximal regularity for local minimizers of non-autonomous functionals, J. Eur. Math. Soc. (JEMS) 24 (2022), no. 4, 1285-1334 (with J. Ok). Get preprint
  2. A proof of Hall's conjecture on length of ray images under starlike mappings of order α, Ann. Fenn. Math. 47 (2022), no. 1, 335-349 (with S. Ponnusamy). (open access) Get preprint
  3. Exploring students' procedural flexibility in three countries, Int. J. STEM Education 9 (2022), article 4 (with J.R. Star, D. Tuomela, N. Joglar Prieto, R. Palkki, M.A. Abánades, J. Pejlare, R.H. Jiang, L. Li and R.-D. Liu). (open access) Dataset

2021

  1. Higher integrability for parabolic systems with Orlicz growth, J. Differential Equations 300 (2021), 925-948 (with J. Ok). Get preprint
  2. Höder continuity of ω-minimizers of functionals with generalized Orlicz growth, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXII (2021), no. 2, 549-582 (with P. Harjulehto and M. Lee). Get preprint
  3. Double phase image restoration, J. Math. Anal. Appl. 501 (2021), no. 1, article 123832 (with P. Harjulehto). Get preprint
  4. The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth, J. Differential Equations 275 (2021), 790-814 (with A. Benyaiche, P. Harjulehto and A. Karppinen). Get preprint

2020

  1. Characterization of generalized Orlicz spaces, Commun. Contemp. Math. 22 (2020), no. 02, article 1850079 (with R. Ferreira and A. Ribeiro). Get preprint

2019

  1. Finnish students' flexibility and its relation to speed and accuracy in equation solving, Nordic Studies Math. Education NOMAD 24 (2019), no. 3-4, 43-58 (with R. Palkki). Get preprint
  2. Extension in generalized Orlicz spaces, Nonlinear Studies 26 (2019), no. 4 (Lars-Erik Persson Anniversary Special Issue), 861-868 (with P. Harjulehto). Get preprint
  3. Calderʫn-Zygmund estimates in generalized Orlicz spaces, J. Differential Equations 267 (2019), no. 5, 2792-2823 (with J. Ok). Get preprint
  4. Relationship between mathematical flexibility and success in national examinations, Eur. J. Sci. Math. Education 7 (2019), no. 1, 1-13 (with R. Palkki, J. Star and D. Tuomela). (open access) Get preprint
  5. Boundary regularity under generalized growth conditions, Z. Anal. Anwendungen 38 (2019), no. 1, 73-96 (with P. Harjulehto). Get preprint

2018

  1. Mathematics teachers' reasons to use (or not) intentional errors, Teaching Math. Computer Sci. 16 (2018), no. 2, 263-282 (with R. Palkki). Get preprint
  2. Uniform convexity and associate spaces, Czechosolvak Math. J. 68 (2018), no. 4, 1011-1020 (with P. Harjulehto). Get preprint
  3. Local higher integrability of the gradient of a quasiminimizer under generalized Orlicz growth conditions, Nonlinear Anal. 177 (2018), 543-552 (Special issue in honor of Carlo Sbordone) (with P. Harjulehto and A. Karppinen). Get preprint
  4. Capacities in generalized Orlicz spaces, J. Function Spaces 2018, Article ID 8459874, 10 pages (with D. Baruah and P. Harjulehto). (open access) Get preprint
  5. Homogeneous variable exponent Besov and Triebel-Lizorkin spaces, Math. Nachr. 291 (2018), no.8-9, 1177-1190 (with A. Almeida and L. Diening). Get preprint
  6. Extrapolation and interpolation in generalized Orlicz spaces, Trans. Amer. Math. Soc. 370 (2018), no. 6, 4323-4349 (with D. Cruz-Uribe). Get preprint

2017

  1. The Riesz potential in generalized Orlicz spaces, Forum Math. 29 (2017), no. 1, 229-244 (with P. Harjulehto). Get preprint
  2. Höder regularity of quasiminimizers under generalized growth conditions, Calc. Var. Partial Differential Equations, 56 (2017), article 22 (with P. Harjulehto and O. Toivanen). Get preprint
  3. Characterization of the variable exponent Sobolev norm without derivatives, Commun. Contemp. Math. 19 (2017), no. 3, 1650022 (with A. Ribeiro). Get preprint

2016

  1. Geometric properties of φ-uniform domains, J. Anal. 24 (2016), no. 1, 57-66 (with R. Klén, S.K. Sahoo and M. Vuorinen). Get preprint
  2. Generalized Orlicz spaces and related PDE, Nonlinear Anal. 143 (2016), 155-173 (with P. Harjulehto and R. Klén). Get preprint
  3. Solution of two conjectures of Klén, Lindén, Vuorinen and Wang, Comput. Methods Funct. Theory 16 (2016), no. 2, 283-286 (with R. Klén). Get preprint
  4. Corrigendum to "The maximal operator on generalized Orlicz spaces" [J. Funct. Anal. 269 (2015) 4038-4048], J. Funct. Anal. 271 (2016), no. 1, 240-243. (open access) Get preprint

2015

  1. The maximal operator on generalized Orlicz spaces, J. Funct. Anal. 269 (2015), no. 12, 4038-4048. (open access) Get preprint corrections (Dec 2015)
  2. Promoting exploratory teaching in mathematics: A design experiment on a CPD course for teachers, LUMAT 3 (2015), no. 6 (with H. Heikkinen, V. Kangas & M. Leinonen). Get preprint
  3. Point-wise behavior of the Geman-McClure and the Hebert-Leahy image restoration models, Inverse Probl. Imaging 9 (2015), no. 3, 835-851 (with P. Harjulehto and J. Tiirola). Get preprint
  4. Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces, Math. Scand. 116 (2015), no. 1, 5-22 (with T. Adamowicz and P. Harjulehto). (open access) Get preprint
  5. Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces, Ann. Mat. Pura Appl. 194 (2015) no. 2, 405-424 (with A. Almeida, P. Harjulehto and T. Lukkari). (open access) Get preprint

2014

  1. Interpolation in variable exponent spaces, Rev. Mat. Complut. 27 (2014), no. 2, 657-676 (with A. Almeida). (open access) Get preprint

2013

  1. Development and awareness of function understanding in first year university students, Proceedings of the Eight Congress of the European Society for Research in Mathematics Education (eds. B. Ubuz, C. Haser, M. Mariotti), 2013, 2366-2375, Ankara, Turkey: European Society for Research in Mathematics Education (with O. Hyväinen and T. Vedenjuoksu). Get preprint
  2. Critical variable exponent functionals in image restoration, Appl. Math. Letters 26 (2013), 56-60 (with P. Harjulehto, V. Latvala and O. Toivanen). (open access) Get preprint

2012

  1. Matematiikan didaktiikkaa tutkimuksen valossa - kohti kansainväisyyttä Ainedidaktinen kokoomateos, Ainedidaktiikka tutkimuskohteena ja tiedonalana (eds. A. Kallioniemi and A. Virta), 2012, 250-271, Jyväkylä: Finnish Educational Research Association (with H. Krzywacki, A. Laine and M.S. Hannula). Get preprint
  2. Convex sets of constant width and 3-diameter, Houston J. Math. 38 (2012), no. 2, 421-443 (with Z. Ibragimov and D. Minda). Get preprint
  3. Gromov hyperbolicity of Denjoy domains through fundamental domains, Publ. Math. Debrecen 80 (2012), no. 3-4, 295-310 (with A. Portilla, E. Tourís and J. M. Rodríguez). Get preprint
  4. Gromov hyperbolicity of the hyperbolic and quasihyperbolic metrics, J. Math. Soc. Japan 64 (2012), no. 1, 245-259 (with H. Lindén, A. Portilla, E. Tourís and J. M. Rodríguez). (open access) Get preprint

2011

  1. The strong minimum principle for quasisuperminimizers of non-standard growth, Ann. Inst. H. Poincare Anal. Non Lineaire 28 (2011), no. 5, 731-742 (with P. Harjulehto, V. Latvala and O. Toivanen). (open access) Get preprint
  2. Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian, Complex Var. Elliptic Equ. 56 (2011), no. 5-6, 643-657 (with P. Harjulehto and V. Latvala). Get preprint
  3. Iterated maximal functions in variable exponent Lebesgue spaces, Manuscripta Math. 135 (2011), no. 3-4, 381-399 (with P. Harjulehto, Y. Mizuta and T. Shimomura). Get preprint
  4. The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14 (2011), no. 3, 361-374 (with D. Cruz-Uribe and L. Diening). (open access) Get preprint
  5. Uniformly separated sets and Gromov hyperbolicity of domains with the quasihyperbolic metric, Mediterr. J. Math. 8 (2011), no. 1, 47-65 (with A. Portilla, E. Tourís and J. M. Rodríguez). Get preprint
  6. Harnack's inequality and the strong p(x)-Laplacian, J. Differential Equations 250 (2011), no. 3, 1631-1649 (with T. Adamowicz). (open access) Get preprint

2010

  1. Equivalence of the Apollonian and its inner metric, Int. J. Math. Math. Sci. (2010), Article ID 191858 (with S. Ponnusamy and S. Sahoo). (open access) Get preprint
  2. Mappings of finite distortion and PDE with nonstandard growth, Int. Math. Res. Not. IMRN (2010), 1940-1965 (with T. Adamowicz). Get preprint
  3. Overview of differential equations with non-standard growth, Nonlinear Anal. 72 (2010), no. 12, 4551-4574 (with P. Harjulehto, U. V. Le and M. Nuortio). Get preprint
  4. Sobolev inequalities for Orlicz spaces of two variable exponents, Glasgow Math. J. 52 (2010), 227-240 (with Y. Mizuta, T. Ohno and T. Shimomura). (open access) Get preprint
  5. Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains, Bull. London Math. Soc. 42 (2010), no. 2, 282-294 (with A. Portilla, E. Tourís and J. M. Rodríguez). Get preprint
  6. Starlikeness of the Gaussian hypergeometric function, Complex Var. Elliptic Equ. 55 (2010), no. 1-2, 173-184 (with S. Ponnusamy and M. Vuorinen). Get preprint
  7. Comparative Gromov hyperbolicity results for the hyperbolic and quasiyperbolic metrics, Complex Var. Elliptic Equ. 55 (2010), no. 1-2, 127-135 (with A. Portilla, E. Tourís and J. M. Rodríguez). Get preprint
  8. Besov spaces with variable smoothness and integrability, J. Funct. Anal 258 (2010), no. 5, 1628-1655 (with A. Almeida). (open access) Get preprint
  9. Packing sets of patterns, European J. Combin. 31 (2010), no. 1, 241-253 (with A. Burstein). (open access) Get preprint

2009

  1. Further results on variable exponent trace spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr & Nicolosi (ed.)), World Scientific, 2009, 101-106 (with L. Diening). Get preprint
  2. Variable exponent spaces on metric measure spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr & Nicolosi (ed.)), World Scientific, 2009, 107-121 (with T. Futamura, P. Harjulehto, Y. Mizuta and T. Shimomura). Get preprint
  3. Maximal functions in variable exponent spaces: limiting cases of the exponent, Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 2, 503-522 (with L. Diening, P. Harjulehto, Y. Mizuta and T. Shimomura). (open access) Get preprint
  4. Local-to-global results in variable exponent spaces, Math. Res. Letters 16 (2009), no. 2, 263-278. (open access) Get preprint
  5. Function spaces of variable integrability and differentiability, J. Funct. Anal. 256 (2009), no. 6, 1731-1768 (with L. Diening and S. Roudenko). (open access) Get preprint
  6. Harnack's inequality for p(·)-harmonic functions with unbounded exponent p, J. Math. Anal. Appl. 352 (2009), no. 1, 345-359 (with P. Harjulehto and V. Latvala). (open access) Get preprint

2008

  1. Sobolev inequalities for variable exponents attaining the values 1 and n, Publ. Mat. 52 (2008), 347-363 (with P. Harjulehto). (open access) Get preprint
  2. Minimizers of the variable exponent, non-uniformly convex Dirichlet energy, J. Math. Pures Appl. (9) 89 (2008), no. 2, 174-197 (with P. Harjulehto and V. Latvala). (open access) Get preprint

2007

  1. The p(x)-Laplacian and applications, J. Anal. 15 (2007), 53-62 (Special proceedings volume). (open access)
  2. Variable exponent trace spaces, Studia Math. 183 (2007), no. 2, 127-141 (with L. Diening). (open access) Get preprint
  3. Peer-assessment in mathematics at NTNU, Relating Practice and Research in Mathematics Education (NORMA 05, Trondheim, Norway, 2005), 469-473, Tapir Press, Tronheim, Norway, 2007 (with K. Hag). Get preprint
  4. Obstacle problems and superharmonic functions with nonstandard growth, Nonlinear Anal. 67 (2007), no. 12, 3424-3440 (with P. Harjulehto, M. Koskenoja, T. Lukkari and N. Marola). Get preprint
  5. Isometries of hyperbolic type lenght metrics and the medial axis, In the Tradition of Ahlfors-Bers, IV (Ann Arbor, MI, 2005), 63-74, Contemp. Math. 432, Amer. Math. Soc., Providence, RI, 2007. (with Z. Ibragimov, D. Minda, S. Ponnusamy and S. K. Sahoo). Get preprint
  6. Properties of capacities in variable exponent Sobolev spaces, J. Anal. Appl. 5 (2007), no. 2, 71-92. (with P. Harjulehto and M. Koskenoja). Get preprint
  7. Isometries of the quasihyperbolic metric, Pacific J. Math. 230 (2007), no. 2, 315-326. (open access) Get preprint
  8. Inequalities of generalized hyperbolic metrics, Rocky Mountain J. Math. 37 (2007), no. 1, 189-202. (open access) Get preprint
  9. On the density of smooth functions in variable exponent Sobolev space, Rev. Mat. Iberoamericana 23 (2007), no. 1, 215-237. (open access) Get preprint
  10. The maximal function on Lebesgue spaces with variable exponent approaching 1, Math. Nachr. 280 (2007), no. 1-2, 74-82. Get preprint
  11. Apollonian isometries of regular domains are Möbius mappings, Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 1, 83-98 (with Z. Ibragimov). (open access) Get preprint

2006

  1. Variable exponent Sobolev spaces on metric measure spaces, Funct. Approx. Comment. Math. 36 (2006), 79-94 (with P. Harjulehto and M. Pere). (open access) Get preprint
  2. Inequalities and geometry of the Apollonian and related metrics, Rev. Roumaine Math. Pures Appl. 51 (2006), no. 4, 433-452 (with S. Ponnusamy and S. K. Sahoo). Get preprint
  3. The Apollonian metric: the comparison property, bilipchitz mappings and thick sets, J. Appl. Anal. 12 (2006), no. 2, 209-232. Get preprint
  4. The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal. 25 (2006), no. 3, 205-222 (with P. Harjulehto, M. Koskenoja and S. Varonen). Get preprint
  5. Sobolev embeddings in metric measure spaces with variable dimension, Math. Z. 254 (2006), no. 3, 591-609 (with P. Harjulehto and V. Latvala). Get preprint
  6. On the variable exponent Dirichlet energy integral, Comm. Pure Appl. Anal. 5 (2006), no 3, 413-420. Get preprint
  7. Some inequalities related to the analysis of electricity auctions, Appl. Math. Letters 19 (2006), no. 8, 814-819 (with P. Holmberg). (open access) Get preprint
  8. Statistical manifold as an affine space: A functional equation approach, J. Math. Psych. 50 (2006), no. 1, 60-65 (with J. Zhang). Get preprint
  9. Isometries of relative metrics, Comput. Methods Function Theory 6 (2006), no. 1, 15-28 (with H. Lindén and Z. Ibragimov). Get preprint
  10. Gromov hyperbolicity of the jG and j~G metrics, Proc. Amer. Math. Soc. 134 (2006), 1137-1142. (open access) Get preprint

2005

  1. Hardy's inequality in variable exponent Sobolev spaces, Georgian Math. J. 12 (2005), no. 3, 431-442 (with P. Harjulehto and M. Koskenoja). Get preprint
  2. Variable Sobolev capacity and the assumptions on the exponent, Orlicz Centenary Volume II, Banach Center Publ. 68 (2005), 51-59 (with P. Harjulehto, M. Koskenoja and S. Varonen). Get preprint
  3. Lebesgue points in variable exponent Sobolev spaces on metric measure spaces, Complex Analysis and Free Boundary Flows, Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 2004, vol. 1, no. 3, 87-99 (with P. Harjulehto and V. Latvala). Get preprint
  4. Apollonian isometries of planar domains are Möbius mappings, J. Geom. Anal. 15 (2005), no. 2, 229-237 (with Z. Ibragimov). Get preprint
  5. Open problems in variable exponent Lebesgue and Sobolev spaces, FSDONA04 Proceedings (Drabek and Rakosnik (eds.); Milovy, Czech Republic, 2004) 38-48 (with L. Diening and A. Nekvinda). Get preprint
  6. Variable exponent Lebesgue spaces on metric spaces: the Hardy-Littlewood maximal operator, Real Anal. Exchange 30 (2004), no. 1, 87-104 (with P. Harjulehto and M. Pere). (open access) Get preprint
  7. Counter-examples of regularity in variable exponent Sobolev spaces, The $p$-Harmonic Equation and Recent Advances in Analysis (Manhattan, KS, 2004), 133-143, Contemp. Math. 367, Amer. Math. Soc., Providence, RI, 2005. Get preprint
  8. A New Weighted Metric: the Relative Metric II, J. Math. Anal. Appl. 301 (2005), no. 2, 336-353. (open access) Get preprint
  9. The Apollonian metric: quasi-isotropy and Seittenranta's metric, Comput. Methods Funct. Theory 4 (2005), no. 2, 249-273.

2004

  1. Lebesgue points in variable exponent spaces, Ann. Acad. Sci. Fenn. Math. 29 (2004), 295-306 (with P. Harjulehto). (open access)
  2. The Apollonian inner metric, Comm. Anal. Geom. 12 (2004), no. 4, 927-947. (open access)
  3. Isometries of the half-apollonian metric, Complex Var. Theory Appl. 49 (2004), 405-415 (with H. Lindén). Get preprint
  4. Fuglede's theorem in variable exponent Sobolev space, Collect. Math. 55,3 (2004), 315-324 (with P. Harjulehto and O. Martio). (open access)
  5. A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces, Rev. Mat. Complut. 17 (2004), 129-146 (with P. Harjulehto). (open access)
  6. Optimal inequalities between Seiffert's mean and power means, Math. Inequal. Appl. 7 (2004), 47-53. Get preprint

2003

  1. An overview of variable exponent Lebesgue and Sobolev spaces, Future Trends in Geometric Function Theory (D. Herron (ed.), RNC Workshop, Jyväskylä, 2003), 85-93 (with P. Harjulehto). Get preprint
  2. The Apollonian metric: limits of the comparison and bilipschitz properties, Abstr. Appl. Anal. 2003, no. 20, 1141-1158. (open access)
  3. The Dirichlet energy integral on intervals in variable exponent Sobolev spaces, Z. Anal. Anwendungen 22 (2003), no. 4, 911-923 (with P. Harjulehto and M. Koskenoja). (open access)
  4. Sobolev capacity on the space W1,p(·)(Rn), J. Funct. Spaces Appl. 1 (2003), no. 1, 17-33 (with P. Harjulehto, M. Koskenoja and S. Varonen). (open access)
  5. The Apollonian metric: uniformity and quasiconvexity, Ann. Acad. Sci. Fenn. Math. 28 (2003), 385-414. (open access)
  6. Packing patterns into words, Electron. J. Comb. 9(2) (2002-2003), #R20 (with A. Burstein and T. Mansour; 13 pp.). (open access)
  7. Distortion in the spherical metric under quasiconformal mappings, Conform. Geom. Dyn. 7 (2003), 1-10. (open access) Get preprint

2002

  1. The packing density of other layered permutations, Electron. J. Comb. 9(2) (2002-2003), #R1 (16 pp.). (open access)
  2. A monotonicity property of ratios of symmetric homogeneous means, J. Inequal. Pure Appl. Math. 3(5) (2002), Article 71. (open access)
  3. A New Weighted Metric: the Relative Metric I, J. Math. Anal. Appl. 274 (2002), no. 1, 38-58. (open access) Get preprint

2000

  1. On Descents in Standard Young Tableaux, Electron. J. Comb. 7 (2000), #R57 (13 pp.). (open access) Get preprint

Unpublished

  1. On the effects of residual structure on factor congruence following Procrustes rotation (with J. Lönnqvist). Get preprint
  2. Muckenhoupt weights in variable exponent spaces (with L. Diening). Get preprint