Peter Hästö's Publications
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Books
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mathematicians under the year 2003.

Lebesgue and Sobolev spaces with variable exponents,
Lecture Notes in Mathematics, vol. 2017,
SpringerVerlag, 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).

Which one is the "best"? A crossnational 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).
Dataset

Minimizers of abstract generalized Orliczbounded variation energy,
Math. Methods Appl. Sci.,
to appear (Xianling Fan Anniversary Special Issue)
(with M. Eleuteri and P. Harjulehto).

Riesz spaces with generalized Orlicz growth,
submitted
(with J. Juusti and H. Rafeiro).

Regularity theory for nonautonomous problems with a priori assumptions,
submitted
(with J. Ok).

Bounded variation spaces with generalized Orlicz growth related to image denoising,
submitted
(with M. Eleuteri and P. Harjulehto).

A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces,
J. Geom. Anal. 33 (2023), article 7.

Bloch estimates in nondoubling generalized Orlicz spaces,
Math. Eng. 5 (2023), no. 3, 121 (Giuseppe Mingione Anniversary Special Issue)
(with P. Harjulehto and J. Juusti).

Procedural flexibility in early university mathematics,
FMSERA Journal 5 (2022), 4660
(with A.M. ErnvallHytönen, H. Krzywacki and S. Parikka).

Regularity theory for nonautonomous partial differential equations without Uhlenbeck structure,
Arch. Ration. Mech. Anal. 245 (2022), no. 3, 14011436
(with J. Ok).

Maximal regularity for local minimizers of nonautonomous functionals,
J. Eur. Math. Soc. (JEMS) 24 (2022), no. 4, 12851334
(with J. Ok).

A proof of Hall's conjecture on length of ray images under starlike mappings of order α,
Ann. Fenn. Math. 47 (2022), no. 1, 335349
(with S. Ponnusamy).

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

Higher integrability for parabolic systems with Orlicz growth,
J. Differential Equations 300 (2021), 925948
(with J. Ok).

Höder continuity of ωminimizers
of functionals with generalized Orlicz growth,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXII (2021), no. 2, 549582
(with P. Harjulehto and M. Lee).

Double phase image restoration,
J. Math. Anal. Appl. 501 (2021), no. 1, article 123832
(with P. Harjulehto).

The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth,
J. Differential Equations 275 (2021), 790814
(with A. Benyaiche, P. Harjulehto and A. Karppinen).

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

Finnish students' flexibility and its relation to speed and accuracy in equation solving,
Nordic Studies Math. Education NOMAD 24 (2019), no. 34, 4358
(with R. Palkki).

Extension in generalized Orlicz spaces,
Nonlinear Studies 26 (2019),
no. 4 (LarsErik Persson Anniversary Special Issue), 861868
(with P. Harjulehto).

CalderónZygmund estimates in generalized Orlicz spaces,
J. Differential Equations 267 (2019), no. 5, 27922823 (with J. Ok).

Relationship between mathematical flexibility and success in national examinations,
Eur. J. Sci. Math. Education 7 (2019), no. 1, 113
(with R. Palkki, J. Star and D. Tuomela).

Boundary regularity under generalized growth conditions,
Z. Anal. Anwendungen 38 (2019), no. 1, 7396
(with P. Harjulehto).

Mathematics teachers' reasons to use (or not) intentional errors,
Teaching Math. Computer Sci.
16 (2018), no. 2, 263282
(with R. Palkki).

Uniform convexity and associate spaces,
Czechosolvak Math. J. 68 (2018), no. 4, 10111020
(with P. Harjulehto).

Local higher integrability of the gradient of a quasiminimizer under generalized Orlicz growth conditions,
Nonlinear Anal. 177 (2018), 543552 (Special issue in honor of Carlo Sbordone)
(with P. Harjulehto and A. Karppinen).

Capacities in generalized Orlicz spaces,
J. Function Spaces 2018, Article ID 8459874, 10 pages
(with D. Baruah and P. Harjulehto).

Homogeneous variable exponent Besov and TriebelLizorkin spaces,
Math. Nachr.
291 (2018), no.89, 11771190
(with A. Almeida and L. Diening).

Extrapolation and interpolation in generalized Orlicz spaces,
Trans. Amer. Math. Soc.
370 (2018), no. 6, 43234349 (with D. CruzUribe).

The Riesz potential in generalized Orlicz spaces,
Forum Math.
29 (2017), no. 1, 229244
(with P. Harjulehto).

Höder regularity of quasiminimizers under generalized growth conditions,
Calc. Var. Partial Differential Equations,
56 (2017), article 22 (with P. Harjulehto and O. Toivanen).

Characterization of the variable exponent Sobolev norm without derivatives,
Commun. Contemp. Math. 19 (2017), no. 3, 1650022 (with A. Ribeiro).

Geometric properties of φuniform domains,
J. Anal. 24 (2016), no. 1, 5766
(with R. Klén, S.K. Sahoo and M. Vuorinen).

Generalized Orlicz spaces and related PDE,
Nonlinear Anal. 143 (2016), 155173
(with P. Harjulehto and R. Klén).

Solution of two conjectures of Klén, Lindén, Vuorinen and Wang,
Comput. Methods Funct. Theory
16 (2016), no. 2, 283286
(with R. Klén).

Corrigendum to "The maximal operator on generalized Orlicz spaces" [J. Funct. Anal. 269 (2015) 40384048],
J. Funct. Anal. 271 (2016), no. 1,
240243.

The maximal operator on generalized Orlicz spaces,
J. Funct.
Anal. 269 (2015), no. 12, 40384048.
corrections (Dec 2015)

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).

Pointwise behavior of the GemanMcClure and the HebertLeahy image restoration models,
Inverse Probl. Imaging 9 (2015), no. 3, 835851
(with P. Harjulehto and J. Tiirola).

Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces,
Math. Scand. 116 (2015), no. 1, 522
(with T. Adamowicz and P. Harjulehto).

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces,
Ann. Mat. Pura Appl. 194 (2015)
no. 2, 405424
(with A. Almeida, P. Harjulehto and T. Lukkari).

Interpolation in variable exponent spaces,
Rev. Mat. Complut. 27 (2014), no. 2, 657676
(with A. Almeida).

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, 23662375,
Ankara, Turkey: European Society for Research in Mathematics Education
(with O. Hyväinen and T. Vedenjuoksu).

Critical variable exponent functionals in image restoration,
Appl. Math. Letters
26 (2013), 5660
(with P. Harjulehto, V. Latvala and O. Toivanen).

Matematiikan didaktiikkaa tutkimuksen valossa  kohti kansainväisyyttä
Ainedidaktinen kokoomateos,
Ainedidaktiikka tutkimuskohteena ja tiedonalana (eds. A. Kallioniemi and A. Virta), 2012,
250271,
Jyväkylä: Finnish Educational Research Association
(with H. Krzywacki, A. Laine and M.S. Hannula).

Convex sets of constant width and 3diameter,
Houston J. Math. 38 (2012), no. 2, 421443
(with Z. Ibragimov and D. Minda).

Gromov hyperbolicity of Denjoy domains through fundamental domains,
Publ. Math. Debrecen
80 (2012), no. 34, 295310
(with A. Portilla, E. Tourís and J. M. Rodríguez).

Gromov hyperbolicity of the hyperbolic and quasihyperbolic metrics,
J. Math. Soc. Japan 64 (2012), no. 1, 245259
(with H. Lindén, A. Portilla, E. Tourís and J. M. Rodríguez).

The strong minimum principle for quasisuperminimizers of nonstandard growth,
Ann. Inst. H. Poincare Anal. Non Lineaire
28 (2011), no. 5, 731742
(with P. Harjulehto, V. Latvala and O. Toivanen).

Boundedness of solutions of the nonuniformly convex, nonstandard growth Laplacian,
Complex Var. Elliptic Equ.
56 (2011), no. 56, 643657
(with P. Harjulehto and V. Latvala).

Iterated maximal functions in variable exponent Lebesgue spaces,
Manuscripta Math. 135 (2011), no. 34, 381399
(with P. Harjulehto, Y. Mizuta and T. Shimomura).

The maximal operator on weighted variable Lebesgue spaces,
Fract. Calc. Appl. Anal. 14 (2011), no. 3, 361374
(with D. CruzUribe and L. Diening).

Uniformly separated sets and Gromov hyperbolicity of domains
with the quasihyperbolic metric, Mediterr.
J. Math. 8 (2011), no. 1, 4765
(with A. Portilla, E. Tourís and J. M. Rodríguez).

Harnack's inequality and the strong p(x)Laplacian,
J. Differential Equations
250 (2011), no. 3, 16311649
(with T. Adamowicz).

Equivalence of the Apollonian and its inner metric,
Int. J. Math. Math. Sci. (2010), Article ID 191858
(with S. Ponnusamy and S. Sahoo).

Mappings of finite distortion and PDE with nonstandard growth,
Int. Math. Res. Not. IMRN (2010), 19401965
(with T. Adamowicz).

Overview of differential equations with nonstandard growth,
Nonlinear Anal. 72 (2010), no. 12, 45514574
(with P. Harjulehto, U. V. Le and M. Nuortio).

Sobolev inequalities for Orlicz spaces of two variable exponents,
Glasgow Math. J. 52 (2010), 227240
(with Y. Mizuta, T. Ohno and T. Shimomura).

Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains,
Bull.
London Math. Soc. 42 (2010), no. 2, 282294
(with A. Portilla, E. Tourís and J. M. Rodríguez).

Starlikeness of the Gaussian hypergeometric function,
Complex Var.
Elliptic Equ. 55 (2010), no. 12, 173184
(with S. Ponnusamy and M. Vuorinen).

Comparative Gromov hyperbolicity results for the hyperbolic and
quasiyperbolic metrics,
Complex Var. Elliptic Equ. 55 (2010), no. 12, 127135
(with A. Portilla, E. Tourís and J. M. Rodríguez).

Besov spaces with variable smoothness and integrability,
J. Funct. Anal
258 (2010), no. 5, 16281655 (with A. Almeida).

Packing sets of patterns,
European J. Combin. 31 (2010), no. 1, 241253
(with A. Burstein).

Further results on variable exponent trace spaces,
More progresses in analysis (ISAAC5, Catania, 2005, Begehr & Nicolosi (ed.)),
World Scientific, 2009, 101106 (with L. Diening).

Variable exponent spaces on metric measure spaces,
More progresses in analysis (ISAAC5, Catania, 2005, Begehr & Nicolosi (ed.)),
World Scientific, 2009, 107121
(with T. Futamura, P. Harjulehto, Y. Mizuta and T. Shimomura).

Maximal functions in variable exponent spaces: limiting cases of the exponent,
Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 2, 503522
(with L. Diening, P. Harjulehto, Y. Mizuta and T. Shimomura).

Localtoglobal results in variable exponent spaces,
Math. Res. Letters
16 (2009), no. 2, 263278.

Function spaces of variable integrability and differentiability,
J. Funct. Anal. 256 (2009), no. 6, 17311768
(with L. Diening and S. Roudenko).

Harnack's inequality for p(·)harmonic functions
with unbounded exponent p,
J. Math. Anal. Appl. 352 (2009), no. 1, 345359
(with P. Harjulehto and V. Latvala).

Sobolev inequalities for variable exponents attaining the values 1 and n,
Publ. Mat. 52 (2008), 347363
(with P. Harjulehto).

Minimizers of the variable exponent, nonuniformly convex Dirichlet energy,
J. Math. Pures Appl. (9) 89 (2008), no. 2, 174197
(with P. Harjulehto and V. Latvala).

The p(x)Laplacian and applications,
J. Anal. 15 (2007), 5362 (Special proceedings volume).

Variable exponent trace spaces,
Studia Math. 183 (2007), no. 2, 127141
(with L. Diening).

Peerassessment in mathematics at NTNU,
Relating Practice and Research in Mathematics Education
(NORMA 05, Trondheim, Norway, 2005), 469473, Tapir Press, Tronheim, Norway, 2007
(with K. Hag).

Obstacle problems and superharmonic functions with nonstandard growth,
Nonlinear Anal. 67 (2007), no. 12, 34243440
(with P. Harjulehto, M. Koskenoja, T. Lukkari and N. Marola).

Isometries of hyperbolic type lenght metrics and the medial axis,
In the Tradition of AhlforsBers, IV (Ann Arbor, MI, 2005), 6374,
Contemp. Math. 432, Amer. Math. Soc., Providence, RI, 2007.
(with Z. Ibragimov, D. Minda, S. Ponnusamy and S. K. Sahoo).
 Properties of capacities in variable exponent Sobolev spaces,
J. Anal. Appl. 5 (2007), no. 2, 7192. (with P. Harjulehto and M. Koskenoja).

Isometries of the quasihyperbolic metric,
Pacific J. Math. 230 (2007), no. 2, 315326.

Inequalities of generalized hyperbolic metrics,
Rocky Mountain J. Math. 37 (2007), no. 1, 189202.
 On the density of smooth functions in variable exponent
Sobolev space, Rev. Mat. Iberoamericana 23 (2007), no. 1, 215237.
 The maximal function on Lebesgue spaces with
variable exponent approaching 1,
Math. Nachr. 280 (2007), no. 12, 7482.
 Apollonian isometries of regular domains are Möbius
mappings,
Ann. Acad. Sci. Fenn. Math. 32 (2007),
no. 1, 8398 (with Z. Ibragimov).
 Variable exponent Sobolev spaces on metric measure spaces,
Funct. Approx. Comment. Math. 36 (2006), 7994 (with P. Harjulehto and M. Pere).
 Inequalities and geometry of the Apollonian and related metrics,
Rev. Roumaine Math. Pures Appl. 51 (2006), no. 4, 433452 (with S. Ponnusamy and S. K. Sahoo).

The Apollonian metric: the comparison property, bilipchitz mappings and thick sets,
J. Appl. Anal. 12 (2006), no. 2, 209232.

The Dirichlet energy integral and variable exponent Sobolev spaces with zero
boundary values,
Potential Anal.
25 (2006), no. 3, 205222 (with P. Harjulehto, M. Koskenoja and S. Varonen).

Sobolev embeddings in metric measure spaces with variable dimension,
Math. Z. 254 (2006), no. 3, 591609 (with P. Harjulehto and V. Latvala).

On the variable exponent Dirichlet energy integral,
Comm. Pure Appl. Anal. 5 (2006), no 3, 413420.
 Some inequalities related to the analysis of electricity auctions,
Appl. Math. Letters 19 (2006), no. 8, 814819 (with P. Holmberg).

Statistical manifold as an affine space: A functional equation approach,
J. Math. Psych. 50 (2006), no. 1, 6065 (with J. Zhang).
 Isometries of relative metrics,
Comput. Methods Function Theory 6 (2006), no. 1, 1528 (with H. Lindén and Z. Ibragimov).

Gromov hyperbolicity of the j_{G} and j^{~}_{G}
metrics, Proc. Amer. Math. Soc. 134 (2006), 11371142.
 Hardy's inequality in variable exponent Sobolev spaces,
Georgian Math. J. 12 (2005), no. 3, 431442 (with P. Harjulehto and M. Koskenoja).
 Variable Sobolev capacity and the assumptions on the exponent,
Orlicz Centenary Volume II, Banach Center Publ.
68 (2005), 5159 (with P. Harjulehto, M. Koskenoja and S. Varonen).
 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, 8799 (with P. Harjulehto and V. Latvala).
 Apollonian isometries of planar domains are Möbius mappings,
J. Geom. Anal. 15 (2005), no. 2, 229237 (with Z. Ibragimov).
 Open problems in variable exponent Lebesgue and Sobolev spaces,
FSDONA04 Proceedings (Drabek and Rakosnik (eds.); Milovy,
Czech Republic, 2004) 3848 (with L. Diening and A. Nekvinda).

Variable exponent Lebesgue spaces on metric spaces: the HardyLittlewood maximal operator,
Real Anal. Exchange 30 (2004), no. 1, 87104 (with P. Harjulehto and M. Pere).

Counterexamples of regularity in variable exponent Sobolev spaces,
The $p$Harmonic Equation and Recent Advances in Analysis
(Manhattan, KS, 2004), 133143,
Contemp. Math. 367, Amer. Math. Soc., Providence, RI, 2005.

A New Weighted Metric: the Relative Metric II,
J. Math. Anal. Appl. 301 (2005), no. 2, 336353.
 The Apollonian metric: quasiisotropy and Seittenranta's metric,
Comput. Methods Funct. Theory 4 (2005), no. 2, 249273.
 Lebesgue points in variable exponent spaces,
Ann. Acad. Sci. Fenn. Math. 29 (2004), 295306
(with P. Harjulehto).
 The Apollonian inner metric,
Comm. Anal. Geom. 12 (2004), no. 4, 927947.
 Isometries of the halfapollonian metric,
Complex Var. Theory Appl. 49 (2004), 405415
(with H. Lindén).
 Fuglede's theorem in variable exponent Sobolev space,
Collect. Math.
55,3 (2004), 315324
(with P. Harjulehto and O. Martio).

A capacity approach to the Poincaré inequality and Sobolev imbeddings in
variable exponent Sobolev spaces,
Rev. Mat. Complut. 17 (2004), 129146 (with P. Harjulehto).

Optimal inequalities between Seiffert's mean and power means,
Math. Inequal. Appl. 7 (2004), 4753.
 An overview of variable exponent Lebesgue and Sobolev spaces,
Future Trends in Geometric Function Theory
(D. Herron (ed.), RNC Workshop, Jyväskylä, 2003), 8593
(with P. Harjulehto).
 The Apollonian metric: limits of the comparison and bilipschitz properties,
Abstr. Appl. Anal. 2003, no. 20, 11411158.
 The Dirichlet energy integral on intervals in
variable exponent Sobolev spaces,
Z. Anal. Anwendungen 22 (2003), no. 4, 911923
(with P. Harjulehto and M. Koskenoja).

Sobolev capacity on the space W^{1,p(·)}(R^{n}),
J. Funct. Spaces Appl. 1 (2003), no. 1, 1733
(with P. Harjulehto, M. Koskenoja and S. Varonen).

The Apollonian metric: uniformity and quasiconvexity,
Ann. Acad. Sci. Fenn. Math. 28 (2003), 385414.

Packing patterns into words,
Electron. J. Comb. 9(2) (20022003), #R20
(with A. Burstein and T. Mansour; 13 pp.).

Distortion in the spherical metric under quasiconformal mappings,
Conform. Geom. Dyn. 7 (2003), 110.
 The packing density of other layered permutations,
Electron. J. Comb. 9(2) (20022003), #R1 (16 pp.).
 A monotonicity property of ratios of symmetric homogeneous means,
J. Inequal. Pure Appl. Math. 3(5) (2002), Article 71.

A New Weighted Metric: the Relative Metric I,
J. Math. Anal. Appl.
274 (2002), no. 1, 3858.
 On Descents in Standard Young Tableaux,
Electron. J. Comb.
7 (2000), #R57 (13 pp.).

On the effects of residual structure on factor congruence following Procrustes rotation (with J. Lönnqvist).

Muckenhoupt weights in variable exponent spaces
(with L. Diening).