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Unpublished, 2000, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, To appear, Submitted, Books

Click on the -symbol to retrieve a preprint of the publication and the to access it on ArXiv. Some articles are available in open accesss . 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

• Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Mathematics, vol. 2017, Springer-Verlag, Berlin, 2011 (with L. Diening, P. Harjulehto and M. Růžička). Download complete preprint (PDF).
• Orlicz Spaces and Generalized Orlicz Spaces, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019, X+168. (with P. Harjulehto). Download complete preprint (PDF).

Submitted

120. A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains, submitted (with P. Harjulehto and Artur Słabuszewski).
119. Convergence of generalized Orlicz norms with lower growth rate tending to infinity, submitted (with G. Bertazzoni and P. Harjulehto).
118. Strategic flexibility in university mathematics, submitted (with J.R Star).
117. Bounded variation spaces with generalized Orlicz growth related to image denoising, submitted (with M. Eleuteri and P. Harjulehto).
116. Riesz spaces with generalized Orlicz growth, submitted (with J. Juusti and H. Rafeiro).

To appear

115. Regularity theory for non-autonomous problems with a priori assumptions, Calc. Var. Partial Differential Equations, to appear (with J. Ok).
114. Minimizers of abstract generalized Orlicz-bounded variation energy, Math. Methods Appl. Sci., to appear (Xianling Fan Anniversary Special Issue) (with M. Eleuteri and P. Harjulehto).

2023

113. Which one is the "best"? A cross-national comparative study of students' strategy evaluation in equation solving, Int. J. Sci. Math. Education 21 (2023), no. 4, 1127-1151 (with R. Jiang, J. Star, L. Li, R.-D. Liu, D. Tuomela, N. Joglar Prieto, R. Palkki, M. Abánades and J. Pejlare). Dataset
112. A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces, J. Geom. Anal. 33 (2023), article 7.
111. Bloch estimates in non-doubling generalized Orlicz spaces, Math. Eng. 5 (2023), no. 3, 1-21 (Giuseppe Mingione Anniversary Special Issue) (with P. Harjulehto and J. Juusti).

2022

110. Procedural flexibility in early university mathematics, FMSERA Journal 5 (2022), 46-60 (with A.-M. Ernvall-Hytönen, H. Krzywacki and S. Parikka).
109. Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure, Arch. Ration. Mech. Anal. 245 (2022), no. 3, 1401-1436 (with J. Ok).
108. Maximal regularity for local minimizers of non-autonomous functionals, J. Eur. Math. Soc. (JEMS) 24 (2022), no. 4, 1285-1334 (with J. Ok).
107. 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).
106. 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). Dataset

2021

105. Higher integrability for parabolic systems with Orlicz growth, J. Differential Equations 300 (2021), 925-948 (with J. Ok).
104. 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).
103. Double phase image restoration, J. Math. Anal. Appl. 501 (2021), no. 1, article 123832 (with P. Harjulehto).
102. 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).

2020

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

2019

100. 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).
99. Extension in generalized Orlicz spaces, Nonlinear Studies 26 (2019), no. 4 (Lars-Erik Persson Anniversary Special Issue), 861-868 (with P. Harjulehto).
98. Calderón-Zygmund estimates in generalized Orlicz spaces, J. Differential Equations 267 (2019), no. 5, 2792-2823 (with J. Ok).
97. 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).
96. Boundary regularity under generalized growth conditions, Z. Anal. Anwendungen 38 (2019), no. 1, 73-96 (with P. Harjulehto).

2018

95. Mathematics teachers' reasons to use (or not) intentional errors, Teaching Math. Computer Sci. 16 (2018), no. 2, 263-282 (with R. Palkki).
94. Uniform convexity and associate spaces, Czechosolvak Math. J. 68 (2018), no. 4, 1011-1020 (with P. Harjulehto).
93. 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).
92. Capacities in generalized Orlicz spaces, J. Function Spaces 2018, Article ID 8459874, 10 pages (with D. Baruah and P. Harjulehto).
91. Homogeneous variable exponent Besov and Triebel-Lizorkin spaces, Math. Nachr. 291 (2018), no.8-9, 1177-1190 (with A. Almeida and L. Diening).
90. Extrapolation and interpolation in generalized Orlicz spaces, Trans. Amer. Math. Soc. 370 (2018), no. 6, 4323-4349 (with D. Cruz-Uribe).

2017

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

2016

86. Geometric properties of φ-uniform domains, J. Anal. 24 (2016), no. 1, 57-66 (with R. Klén, S.K. Sahoo and M. Vuorinen).
85. Generalized Orlicz spaces and related PDE, Nonlinear Anal. 143 (2016), 155-173 (with P. Harjulehto and R. Klén).
84. Solution of two conjectures of Klén, Lindén, Vuorinen and Wang, Comput. Methods Funct. Theory 16 (2016), no. 2, 283-286 (with R. Klén).
83. 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.

2015

82. The maximal operator on generalized Orlicz spaces, J. Funct. Anal. 269 (2015), no. 12, 4038-4048. corrections (Dec 2015)
81. 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).
80. 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).
79. 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).
78. 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).

2014

77. Interpolation in variable exponent spaces, Rev. Mat. Complut. 27 (2014), no. 2, 657-676 (with A. Almeida).

2013

76. 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).
75. Critical variable exponent functionals in image restoration, Appl. Math. Letters 26 (2013), 56-60 (with P. Harjulehto, V. Latvala and O. Toivanen).

2012

74. 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).
73. Convex sets of constant width and 3-diameter, Houston J. Math. 38 (2012), no. 2, 421-443 (with Z. Ibragimov and D. Minda).
72. 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).
71. 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).

2011

70. 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).
69. 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).
68. 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).
67. 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).
66. 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).
65. Harnack's inequality and the strong p(x)-Laplacian, J. Differential Equations 250 (2011), no. 3, 1631-1649 (with T. Adamowicz).

2010

64. Equivalence of the Apollonian and its inner metric, Int. J. Math. Math. Sci. (2010), Article ID 191858 (with S. Ponnusamy and S. Sahoo).
63. Mappings of finite distortion and PDE with nonstandard growth, Int. Math. Res. Not. IMRN (2010), 1940-1965 (with T. Adamowicz).
62. 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).
61. Sobolev inequalities for Orlicz spaces of two variable exponents, Glasgow Math. J. 52 (2010), 227-240 (with Y. Mizuta, T. Ohno and T. Shimomura).
60. 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).
59. Starlikeness of the Gaussian hypergeometric function, Complex Var. Elliptic Equ. 55 (2010), no. 1-2, 173-184 (with S. Ponnusamy and M. Vuorinen).
58. 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).
57. Besov spaces with variable smoothness and integrability, J. Funct. Anal 258 (2010), no. 5, 1628-1655 (with A. Almeida).
56. Packing sets of patterns, European J. Combin. 31 (2010), no. 1, 241-253 (with A. Burstein).

2009

55. 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).
54. 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).
53. 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).
52. Local-to-global results in variable exponent spaces, Math. Res. Letters 16 (2009), no. 2, 263-278.
51. Function spaces of variable integrability and differentiability, J. Funct. Anal. 256 (2009), no. 6, 1731-1768 (with L. Diening and S. Roudenko).
50. 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).

2008

49. Sobolev inequalities for variable exponents attaining the values 1 and n, Publ. Mat. 52 (2008), 347-363 (with P. Harjulehto).
48. 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).

2007

47. The p(x)-Laplacian and applications, J. Anal. 15 (2007), 53-62 (Special proceedings volume).
46. Variable exponent trace spaces, Studia Math. 183 (2007), no. 2, 127-141 (with L. Diening).
45. 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).
44. 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).
43. 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).
42. Properties of capacities in variable exponent Sobolev spaces, J. Anal. Appl. 5 (2007), no. 2, 71-92. (with P. Harjulehto and M. Koskenoja).
41. Isometries of the quasihyperbolic metric, Pacific J. Math. 230 (2007), no. 2, 315-326.
40. Inequalities of generalized hyperbolic metrics, Rocky Mountain J. Math. 37 (2007), no. 1, 189-202.
39. On the density of smooth functions in variable exponent Sobolev space, Rev. Mat. Iberoamericana 23 (2007), no. 1, 215-237.
38. The maximal function on Lebesgue spaces with variable exponent approaching 1, Math. Nachr. 280 (2007), no. 1-2, 74-82.
37. Apollonian isometries of regular domains are Möbius mappings, Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 1, 83-98 (with Z. Ibragimov).

2006

36. Variable exponent Sobolev spaces on metric measure spaces, Funct. Approx. Comment. Math. 36 (2006), 79-94 (with P. Harjulehto and M. Pere).
35. 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).
34. The Apollonian metric: the comparison property, bilipchitz mappings and thick sets, J. Appl. Anal. 12 (2006), no. 2, 209-232.
33. 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).
32. Sobolev embeddings in metric measure spaces with variable dimension, Math. Z. 254 (2006), no. 3, 591-609 (with P. Harjulehto and V. Latvala).
31. On the variable exponent Dirichlet energy integral, Comm. Pure Appl. Anal. 5 (2006), no 3, 413-420.
30. Some inequalities related to the analysis of electricity auctions, Appl. Math. Letters 19 (2006), no. 8, 814-819 (with P. Holmberg).
29. Statistical manifold as an affine space: A functional equation approach, J. Math. Psych. 50 (2006), no. 1, 60-65 (with J. Zhang).
28. Isometries of relative metrics, Comput. Methods Function Theory 6 (2006), no. 1, 15-28 (with H. Lindén and Z. Ibragimov).
27. Gromov hyperbolicity of the j_G and j^~_G metrics, Proc. Amer. Math. Soc. 134 (2006), 1137-1142.

2005

26. Hardy's inequality in variable exponent Sobolev spaces, Georgian Math. J. 12 (2005), no. 3, 431-442 (with P. Harjulehto and M. Koskenoja).
25. 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).
24. 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).
23. Apollonian isometries of planar domains are Möbius mappings, J. Geom. Anal. 15 (2005), no. 2, 229-237 (with Z. Ibragimov).
22. 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).
21. 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).
20. 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.
19. A New Weighted Metric: the Relative Metric II, J. Math. Anal. Appl. 301 (2005), no. 2, 336-353.
18. The Apollonian metric: quasi-isotropy and Seittenranta's metric, Comput. Methods Funct. Theory 4 (2005), no. 2, 249-273.

2004

17. Lebesgue points in variable exponent spaces, Ann. Acad. Sci. Fenn. Math. 29 (2004), 295-306 (with P. Harjulehto).
16. The Apollonian inner metric, Comm. Anal. Geom. 12 (2004), no. 4, 927-947.
15. Isometries of the half-apollonian metric, Complex Var. Theory Appl. 49 (2004), 405-415 (with H. Lindén).
14. Fuglede's theorem in variable exponent Sobolev space, Collect. Math. 55,3 (2004), 315-324 (with P. Harjulehto and O. Martio).
13. 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).
12. Optimal inequalities between Seiffert's mean and power means, Math. Inequal. Appl. 7 (2004), 47-53.

2003

11. 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).
10. The Apollonian metric: limits of the comparison and bilipschitz properties, Abstr. Appl. Anal. 2003, no. 20, 1141-1158.
9. 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).
8. Sobolev capacity on the space W^1,p(·)(Rⁿ), J. Funct. Spaces Appl. 1 (2003), no. 1, 17-33 (with P. Harjulehto, M. Koskenoja and S. Varonen).
7. The Apollonian metric: uniformity and quasiconvexity, Ann. Acad. Sci. Fenn. Math. 28 (2003), 385-414.
6. Packing patterns into words, Electron. J. Comb. 9(2) (2002-2003), #R20 (with A. Burstein and T. Mansour; 13 pp.).
5. Distortion in the spherical metric under quasiconformal mappings, Conform. Geom. Dyn. 7 (2003), 1-10.

2002

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

2000

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

Unpublished

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