Publications
Books:
P. Harjulehto and P. Hästö: Orlicz Spaces and Generalized Orlicz Spaces, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019, X+169 pages. DOI: 10.1007/978-3-030-15100-3, Download final preprint (PDF), Final version from publisher.
L. Diening, P. Harjulehto, P. Hästö, M. Růžička: Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, vol. 2017, Springer-Verlag, Heidelberg, 2011, X+509 pages, DOI:10.1007/978-3-642-18363-8. Download complete preprint (PDF), Final version from publisher.
Papers:
Recent preprints
P. Harjulehto, P. Hästö and A. Torricelli: Monotonic approximation of differentiable convex functions with applications to general minimization problems. Preprint (arXiv).
P. Harjulehto, P. Hästö and A. Słabuszewski: A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains. Preprint (arXiv).
G. Bertazzoni, P. Harjulehto and P. Hästö: Convergence of generalized Orlicz norms with lower growth rate tending to infinity. Preprint (arXiv).
M. Eleuteri, P. Harjulehto and P. Hästö: Bounded variation spaces with generalized Orlicz growth related to image denoising. Preprint (arXiv).
P. Hästö, J. Juusti and H. Rafeiro: Riesz spaces with generalized Orlicz growth. Preprint (arXiv).
To appear
P. Harjulehto and A. Karppinen: Stability of solutions to obstacle problems with generalized Orlicz growth, Forum Math., to appear. Preprint (arXiv).
M. Eleuteri, P. Harjulehto and P. Hästö: Minimizers of abstract generalized Orlicz-bounded variation energy, Math. Methods Appl. Sci., Special Issue on the occasion of Professor Xianling Fan’s 80th birthday, to appear. Preprint (arXiv).
P. Harjulehto and R. Hurri-Syrjänen: Estimates for the variable order Riesz potential with applications, Potentials & PDEs - The Legacy of David R. Adams, in the book series Advances in Analysis and Geometry, edited by S. Lenhart, and J. Xiao, De Gruyter, to appear.
2023
P. Hästö and J. Ok: Regularity theory for non-autonomous problems with a priori assumptions, Calc. Var. Partial Differential Equations 62 (2023), article 251. Preprint (arXiv), Download from publisher.
P. Harjulehto and R. Hurri-Syrjänen: Estimates for the variable order Riesz potential with applications, in the book Potentials and Partial Differential Equations - The Legacy of David R. Adams (Advances in Analysis and Geometry no. 8) edited by S. Lenhart, and J. Xiao, De Gruyter, 2023, 127-155. Preprint (arXiv), Download from publisher.
J. Juusti: Fuglede's theorem in generalized Orlicz-Sobolev spaces, Collectanea Math. 74 (2023), 299–312. Preprint (arXiv), Download from publisher.
J. Juusti: Extension in generalized Orlicz-Sobolev spaces, J. Math. Anal. Appl. 522 (2023), no. 1, article 126941. Preprint (arXiv), Download from publisher.
P. Hästö: A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces, J. Geom. Anal. 33 (2023), article 7. Preprint (arXiv), Download from publisher.
P. Harjulehto, P. Hästö and J. Juusti: Bloch estimates in non-doubling generalized Orlicz spaces, Math. Eng. 5 (2023), no. 3, 1-21. Special Issue: PDEs and Calculus of Variations – Dedicated to Giuseppe Mingione, on the occasion of his 50th birthday. Preprint (arXiv), Download from publisher.
2022
A. Karppinen and M. Lee: Hölder continuity of the minimizer of an obstacle problem with generalized Orlicz growth, Int. Math. Res. Not. IMRN 2022 (2022), no. 19, 15313-15354. Download from publisher.
P. Hästö and J. Ok: Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure, Arch. Ration. Mech. Anal. 245 (2022), no. 3, 1401-1436. Preprint (arXiv), Download from publisher.
Á. Crespo-Blanco, L. Gasiński, P. Harjulehto and P. Winkert: A new class of double phase variable exponent problems: Existence and uniqueness, J. Differential Equations 323 (2022), 182-228. Preprint (arXiv), Download from publisher.
P. Hästö and J. Ok: Maximal regularity for local minimizers of non-autonomous functionals, J. Eur. Math. Soc. 24 (2022), no. 4, 1285-1334. Preprint (arXiv), Download from publisher.
P. Harjulehto and A. Karppinen: Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces, Ann. Fenn. Math. 47 (2022), no. 1, 489-505. Preprint (arXiv), Download from publisher.
P. Harjulehto and J. Juusti: The Kellogg property under generalized growth conditions, Math. Nachr. 295 (2022), no. 2, 345-362. Preprint (arXiv), Download from publisher.
2021
P. Hästö and J. Ok: Higher integrability for parabolic systems with Orlicz growth, J. Differential Equations 300 (2021), 925-948. Preprint (arXiv), Download from publisher..
P. Harjulehto, P. Hästö and M. Lee: Hölder continuity of \omega-minimizers of functionals with generalized Orlicz growth, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXII (2021), 549-582. Preprint (arXiv), Download from publisher.
P. Harjulehto and P. Hästö: Double phase image restoration, J. Math. Anal. Appl. 501 (2021), no. 1, article 123832. Preprint (arXiv), Download from publisher.
I. Chlebicka and A. Karppinen: Removable sets in elliptic equations with Musielak-Orlicz growth, J. Math. Anal. Appl. 501 (2021), no. 1, article 124073. Preprint(arXiv), Download from publisher.
A. Benyaiche, P. Harjulehto, P. Hästö, A. Karppinen: The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth, J. Differential Equations 275 (2021), 790-814. Preprint (arXiv), Download from publisher.
A. Karppinen: Global continuity and higher integrability of a minimizer of an obstacle under generalized Orlicz growth conditions, Manuscripta Math., 164, 67–94 (2021). Download from publisher.
2020
R. Ferreira, P. Hästö and A. Ribeiro: Characterization of generalized Orlicz spaces, Commun. Contem. Math, 22 (2020), no. 02, article 1850079, Preprint (arxiv), Download from publisher.
2019
P. Harjulehto and P. Hästö: Extension in generalized Orlicz spaces, Nonlinear Studies 26 (2019), no. 4 , 861-868. Special Issue: Lars-Erik Persson 75th Anniversary. Preprint (arxiv).
P. Hästö and J. Ok: Calderón-Zygmund estimates in generalized Orlicz spaces, J. Differential Equations 267 (2019), no. 5, 2792-2823 Preprint (PDF), Download from publisher
P. Harjulehto and P. Hästö: Boundary regularity under generalized growth conditions, Z. Anal. Anwend 38 (2019), no. 1, 73-96 Preprint (PDF), Download from publisher.
2018
P. Harjulehto and P. Hästö: Uniform convexity and associate spaces, Czechoslovak Math. J. 68 (2018), no. 4, 1011-1020. Preprint (PDF), Download from publisher.
A. Almeida, L. Diening and P. Hästö: Homogeneous variable exponent Besov and Triebel-Lizorkin spaces, Math. Nachr. 291 (2018), no. 8-9, 1177-1190. Preprint (PDF), Download from publisher.
P. Harjulehto, P. Hästö and A. Karppinen: 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. Preprint (PDF), Download from publisher.
D. Baruah, P. Harjulehto and P. Hästö: Capacities in generalized Orlicz spaces, J. Funct. Spaces, vol. 2018, Article ID 8459874, 10 pages, 2018. Preprint (PDF), Download from Publisher.
D. Cruz-Uribe and P. Hästö: Extrapolation and interpolation in generalized Orlicz spaces, Trans. Amer. Math. Soc. 370 (2018), no. 6, 4323-4349. Preprint (PDF), Download from Publisher.
2017
P. Hästö and A. Ribeiro: Characterization of the variable exponent Sobolev norm without derivatives, Commun. Contemp. Math. 19 (2017), no. 3, 1650022. Preprint (PDF), Download from Publisher.
V. Latvala and O. Toivanen: Weak Harnack estimates for quasiminimizers with non-standard growth and general structure, Potential Anal. 47 (2017), no. 1, 21–36. Preprint (PDF), Download from Publisher.
P. Harjulehto and P. Hästö: The Riesz potential in generalized Orlicz spaces, Forum Math. 29 (2017), no. 1, 229-244. Preprint (PDF), Download from publisher.
P. Harjulehto, P. Hästö and O. Toivanen: Hölder regularity of quasiminimizers under generalized growth conditions, Calc. Var. Partial Differential Equations 56 (2017), article 22. Preprint (PDF). Download from publisher.
2016
T. Adamowicz and N. Lundström: The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(.)-harmonic measures, Ann. Mat. Pura Appl. (4) 195, Issue 2, 623–658. Download from journal
P. Harjulehto, P. Hästö and R Klén: Basic properties of generalized Orlicz spaces, Nonlinear Anal. 143 (2016), 155-173. Preprint (PDF), Download from publisher.
2015
T. Adamowicz and O. Toivanen: Hölder continuity of quasiminimizers with nonstandard growth, Nonlinear Anal. 125 (2015), 433-456. Download from Arxiv. Download from journal
T. Adamowicz and P. Górka: The Liouville theorems for elliptic equations with nonstandard growth, Comm. Pure Appl. Math. 14 (2015), no. 5, 2377-2392. Download from Arxiv. Download from journal
P. Hästö: The maximal operator on generalized Orlicz spaces, J. Funct. Anal. 269 (2015), no. 12, 4038-4048. Preprint (PDF), Corrections (PDF) , Download from journal
P. Harjulehto, P. Hästö and J. Tiirola: Point-wise behavior of the Geman-McClure and the Hebert-Leahy image restoration models, Inverse Probl. Imaging 9 (2015), no. 3, 835-851. Preprint (PDF), Download from journal.
T. Adamowicz, P. Harjulehto and P. Hästö: Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces, Math. Scand. 116 (2015), no. 1, 5-22. Preprint (PDF).
A. Almeida, P. Harjulehto, P. Hästö and T. Lukkari: Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces, Ann. Mat. Pura Appl. (4) 194 (2015), no. 2, 405-424. Preprint (PDF), Download from journal.
2014
T. Adamowicz, A. Björn, J. Björn: Regularity of p(·)-superharmonic functions, the Kellogg property and semiregular boundary points, Ann. Inst. H. Poincare Anal. Non Lineaire 31 (2014), no. 6, 1131-1153. Preprint (PDF), Download from journal.
T. Adamowicz: Phragmen-Lindelöf theorems for equations with nonstandard growth, Nonlinear Anal. 97 (2014), 169-184. Preprint (PDF), Download from journal.
H. Hakkarainen and M. Nuortio: The variable exponent BV-Sobolev capacity, Rev. Mat. Complut 27 (2014), no. 1, 13-40. Preprint (PDF), Download from journal.
2013
O. Toivanen: Local boundedness of general minimizers with nonstandard growth, Nonlinear Anal., 81 (2013), 62-69. Preprint (PDF), Download from journal.
M. Eleuteri, P. Harjulehto and T. Lukkari: Global regularity and stability of solutions to obstacle problems with nonstandard growth, Rev. Mat. Complut. 26 (2013), 147-181. Preprint (PDF), Download from journal.
P. Harjulehto, V. Latvala and O. Toivanen: A variant of the Geman-McClure -model for image restoration, J. Math. Anal. Appl. 399 (2013), pp. 676-681. Download from journal.
P. Harjulehto, P. Hästö, V. Latvala and O. Toivanen: Critical variable exponent functionals in image restoration, Appl. Math. Lett. 26 (2013), p. 56-60. Preprint (PDF), Download from journal.
2012
O. Toivanen: Harnack's inequality for general solutions with nonstandard growth, Ann. Acad. Sci. Fenn. Math. 37 (2012), 571-577. Preprint (PDF), Download from journal
2011
V. Latvala, T. Lukkari and O. Toivanen: The fundamental convergence theorem for p(·)-superharmonic functions, Potential Anal. 35 (2011), no. 4, 329-351. Prepint (PDF), Download from journal
P. Harjulehto, P. Hästö, V. Latvala and O. Toivanen: The strong minimum principle for quasisuperminimizers of non-standard growth, Ann. Inst. H. Poincare Anal. Non Lineaire 28 (2011), 731-742. Preprint (PDF), Download from journal
P. Harjulehto, P. Hästö and V. Latvala: Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian, Complex Var. Elliptic Equ. 56 (2011), no. 7-9, 643-657. Prepint (PDF) , Download from journal
M. Eleuteri, P. Harjulehto and T. Lukkari: Global regularity and stability of solutions to elliptic equations with nonstandard growth, Complex Var. Elliptic Equ. 56 (2011), no. 7-9, 599-622. Prepint (PDF) , Download from journal
P. Harjulehto, P. Hästö, Y. Mizuta and T. Shimomura: Iterated maximal functions in variable exponent Lebesgue spaces, Manuscripta Math. 135 (2011), no. 3-4, 381-399. Preprint (PDF), Download from journal.
D. Cruz-Uribe, L. Diening and P. Hästö: The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14 (2011), no. 3, 361-374. Preprint(PDF)
J. Keisala: Existence and uniqueness of p(x)-harmonic functions for bounded and unbounded p(x), Licentiate thesis, Rep. Univ. Jyväskylä Dept. Math. Stat. 130 (2011). Download (PDF)
T. Adamowicz and P. Hästö: Harnack's inequality and the strong p(x)-Laplacian, J. Differential Equations 250 (2011), no. 3, 1631-1649. Preprint (PDF), Download from journal
2010
P. Juutinen, T. Lukkari and M. Parviainen: Equivalence of viscosity and weak soluitions for the p(·)-Laplacian, Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010), no. 6, 1471-1478. Prepint (PDF), Download from journal
T. Lukkari, F-Y. Maeda and N. Marola: Wolff potential estimates for elliptic equations with nonstandard growth and applications, Forum Math. 22 (2010), no. 6, 1061-1087 . Prepint (PDF) , Download from journal
T. Lukkari: Boundary continuity of solutions to elliptic equations with nonstandard growth, Manuscripta Math. 132 (2010), no. 3-4, 463-482. Download from journal
T. Adamowicz and P. Hästö: Mappings of finite distortion and PDE with nonstandard growth, Int. Math. Res. Not. (2010), 1940-1965. Prepint (PDF) , Download from journal
P. Hästö, Y. Mizuta, T. Ohno and T. Shimomura: Sobolev inequalities for Orlicz spaces of two variable exponents, Glasgow Math. J. 52 (2010), 227-240. Preprint (PDF)
P. Harjulehto, P. Hästö, U. V. Le and M. Nuortio: Overview of differential equations with non-standard growth, Nonlinear Anal. 72 (2010), 4551-4574. Prepint (PDF) , Download from journal
A. Almeida and P. Hästö: Besov spaces with variable smoothness and integrability, J. Funct. Anal. 258 (2010), no. 5, 1628-1655. Prepint (PDF)
2009
L. Diening and P. Hästö: Further results on variable exponent trace spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr & Nicolosi (ed.)), World Scientific, 2009, 101-106. Preprint (PDF)
T. Futamura, P. Harjulehto, P. Hästö, Y. Mizuta and T. Shimomura: Variable exponent spaces on metric measure spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr & Nicolosi (ed.)), World Scientific, 2009, 107-121. Preprint (PDF)
T. Lukkari: Singular solutions of elliptic equations with nonstandard growth, Math. Nachr. 282 (12) (2009), 1770-1787. Preprint (PDF), Download from journal
L. Diening, P. Harjulehto, P. Hästö, Y. Mizuta, T. Shimomura: Maximal functions in variable exponent spaces: limiting cases of the exponent, Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 2, 503-522. Preprint (PDF) Download from journal
P. Hästö, Local-to-global results in variable exponent spaces, Math. Res. Letters 16 (2009), no. 2, 263-278. Preprint (PDF), Download from journal
L. Diening, P. Hästö and S. Roudenko: Function spaces of variable smoothness and integrability, J. Funct. Anal. 256 (2009), no. 6, 1731-1768. Preprint (PDF), Download from journal
P. Harjulehto, P. Hästö and V. Latvala: Harnack's inequality for p(·)-harmonic functions with unbounded exponent p, J. Math. Anal. Appl. 352 (2009), no. 1, 345-359. Preprint (PDF), Download from journal
2008
P. Harjulehto and P. Hästö: Sobolev inequalities for variable exponents attaining the values 1 and n, Publ. Mat. 52 (2008), no. 2, 347-363. Preprint (PDF), Download from journal
P. Harjulehto and V. Latvala: Fine topology of variable exponent energy superminimizers, Ann. Acad. Sci. Fenn. Math. 33 (2008), 491-510. Preprint (PDF), Download for journal
P. Harjulehto, T. Kuusi, T. Lukkari, N. Marola and M. Parviainen: Harnack's inequality for quasiminimizers with non-standard growth conditions, J. Math. Anal. Appl. 344 (2008), no, 1, 504-520. Preprint (PDF), Download from journal
T. Lukkari: Elliptic equations with nonstandard growth involving measure data, Hiroshima Math. J. 38 (2008), 155-176. Preprint (PDF), Download from journal
P. Harjulehto, P. Hästö and V. Latvala: Minimizers of the variable exponent, non-uniformly convex Dirichlet energy, J. Math. Pures Appl. (9) 89 (2008), no. 2, 174-197. Preprint (PDF), Download from journal, Erratum (PDF)
2007
P. Hästö: The p(x)-Laplacian and applications, J. Anal. 15 (2007), 53-62.
L. Diening and P. Hästö: Variable exponent trace spaces, Studia Math. 183 (2007), no. 2, 127-141. Preprint (PDF)
P. Harjulehto, P. Hästö, M. Koskenoja, T. Lukkari and N. Marola: An obstacle problem and superharmonic functions with nonstandard growth, Nonlinear Anal. 67 (2007), 3424-3440. Preprint (PDF), Download from journal
P. Harjulehto: Variable exponent Sobolev spaces with zero boundary values, Math. Bohem. 132 (2007), no. 2, 125-136. Preprint (PDF)
P. Gurka, P. Harjulehto and A. Nekvinda: Bessel potential spaces with variable exponent, Math. Inequal. Appl. 10 (2007), no. 3, 661-676. Preprint (PDF), Download from journal
P. Harjulehto, P. Hästö and M. Koskenoja: Properties of capacities in variable exponent Sobolev spaces, J. Anal. Appl. 5 (2007), no. 2, 71-92. Preprint (PDF)
P. Harjulehto, J. Kinnunen and K. Tuhkanen: Hölder quasicontinuity in variable exponent Sobolev spaces J. Inequal. Appl. 2007, Article ID 32324, 18 pages, doi:10.1155/2007/32324. Download from journal
P. Hästö: On the density of continuous functions in variable exponent Sobolev space, Rev. Mat. Iberoamericana 23 (2007), no. 1, 215-237.
P. Hästö: The maximal operator in Lebesgue spaces with variable exponent approaching 1, Math. Nachr. 280 (2007), no. 1-2, 74-82. Download from journal
P. Harjulehto, J. Kinnunen and T. Lukkari: Unbounded supersolutions of nonlinear equations with nonstandard growth, Bound. Value Probl. 2007, Article ID 48348, 20 pages, doi:10.1155/2007/48348. Download from journal
2006
P. Harjulehto, P. Hästö and M. Pere: Variable exponent Sobolev spaces on metric measure spaces, Funct. Approx. Comment. Math. 36 (2006), 79--94. Preprint (PDF) and Expanded version (PDF)
P. Harjulehto, P. Hästö, M. Koskenoja and S. Varonen: The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal. 25 (2006), no. 3, 205-222. Preprint (PDF) Download from journal
P. Harjulehto, P. Hästö and V. Latvala: Sobolev embeddings in metric measure spaces with variable dimension, Math. Z. 254 (2006), no. 3, 591-609. Preprint (PDF) Download from journal
P. Hästö: On the variable exponent Dirichlet energy integral, Comm. Pure Appl. Anal. 5 (2006), no. 3, 413-420. Preprint (PDF)
2005
P. Harjulehto, P. Hästö and M. Koskenoja: Hardy's inequality in a variable exponent Sobolev spaces, Georgian Math. J. 12 (2005), no. 3, 431-442. Preprint (PDF)
P. Hästö: 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.
P. Harjulehto, P. Hästö, M. Koskenoja and S. Varonen: Variable Sobolev capacity and the assumptions on the exponent, Orlicz Centenary Volume II, Banach Center Publ. 68 (2005), 51-59. Preprint (PDF)
2004
P. Harjulehto, P. Hästö and V. Latvala: 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. Preprint (PDF)
L. Diening, P. Hästö and A. Nekvinda: Open problems in variable exponent Lebesgue and Sobolev spaces, FSDONA 2004 Proceedings (Drabek and Rakosnik (eds.); Milovy, Czech Republic, 2004) 38-58.
P. Harjulehto and P. Hästö: Lebesgue points in variable exponent spaces, Ann. Acad. Sci. Fenn. Math. 29 (2004), 295-306. Download from journal
P. Harjulehto, P. Hästö and M. Pere: Variable exponent Lebesgue spaces on metric spaces: the Hardy-Littlewood maximal operator, Real Anal. Exchange 30 (2004/2005), no. 1, 87-103. Preprint (PDF)
P. Harjulehto, P. Hästö and O. Martio: Fuglede's theorem in variable exponent Sobolev space, Collect. Math. 55 (2004), no. 3, 315-324. Download from journal
P. Harjulehto and P. Hästö: A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces, Rev. Mat. Complut. 17 (2004), 129-146. Download from journal
2003
P. Harjulehto and P. Hästö: An overview of variable exponent Lebesgue and Sobolev spaces, Future Trends in Geometric Function Theory (D. Herron (ed.), RNC Workshop, Jyväskylä, 2003), 85-94. Preprint (PDF)
P. Harjulehto P. Hästö and M. Koskenoja: The Dirichlet energy integral on intervals in variable exponent Sobolev spaces, Z. Anal. Anwend. 22 (2003), no. 4, 911-923. Download from journal
P. Harjulehto P. Hästö, M. Koskenoja and S. Varonen: Sobolev capacity on the space W1,p(·)(Rn), J. Funct. Spaces Appl. 1 (2003), no. 1, 17-33. Preprint (PDF)