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 complete preprint (PDF), Final version from Springer.
P. Harjulehto, R. Klén and M. Koskenoja: Analyysiä reaaliluvuilla. (A calculus textbook for the first year students.)
Published by Unigrafia, Helsinki, 2014 - 2022, 367 pages, ISBN 978-952-93-4162-7.
At the moment the book is not available. Gaudeamus will publish a new updated edition at 16.9.2023.
Kirjaa ei ole tällä hetkellä saatavilla. Gaudeamus julkaiseen uuden päivitetyn painoksen 16.9.2023.
Download first 56 pages and index (PDF).
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 Springer.
M. Eleuteri, P. Harjulehto and P. Hästö: Bounded variation spaces with generalized Orlicz growth related to image denoising. Get preprint from arXiv
P. Harjulehto and A. Karppinen: Stability of solutions to obstacle problems with generalized Orlicz growth. Get preprint from arXiv
M. Eleuteri, P. Harjulehto and P. Hästö: Minimizers of abstract generalized Orlicz-bounded variation energy, Math. Methods Appl. Sci., Issue on the occasion of Professor Xianling Fan’s 80th birthday, to appear. Get preprint from arXiv, Download from publisher
P. Harjulehto and R. Hurri-Syrjänen: On Choquet integrals and Poincaré-Sobolev inequalities, J. Funct. Anal. 284 (2023), issue 9, paper no. 109862. Get preprint from 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. Get preprint from arXiv Download from publisher
P. Harjulehto and P. Hästö and J. Juusti: Bloch estimates in non-doubling generalized Orlicz spaces, Math. Eng. 5 (2023), issue 3, 1-21. Special Issue: PDEs and Calculus of Variations – Dedicated to Giuseppe Mingione, on the occasion of his 50th birthday. Get preprint from 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 uniquenes, J. Differential Equations 323 (2022), 182-228. Get preprint from 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, 439-505. Get preprint from arXiv, Download from publisher.
P. Harjulehto and J. Juusti: The Kellogg property under generalized growth conditions, Math. Nachr. 295 (2022), issue 2, 345-362. Get preprint from arXiv, Download from publisher.
P. Harjulehto, R. Hurri-Syrjänen, J. Kapulainen and S. Rogovin: On a generalized quasihyperbolic condition in a bounded domain, Math. Rep. (Bucur.), 23(73) (2021), no. 1-2, 157-173. The conference proceedings of RomFin2019 and FSDONA2019. Preprint (PDF), Download from publisher.
P. Harjulehto, P. Hästö and M. Lee: Hölder continuity of ω-minimizers of functionals with generalized Orlicz growth, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXII (2021), issue 2, 549-582. Get preprint from arXiv, Download from publisher.
P. Harjulehto and P. Hästö: Double phase image restoration, J. Math. Anal. Appl. 501 (2021), issue 1, article 123832. Get preprint from 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. Get preprint from arXiv, Download from publisher.
P. Harjulehto and P. Hästö: Extension in generalized Orlicz spaces, Nonlinear Studies 26 (2019), no.4, 861-868, Lars-Erik Persson Anniversary Special Issue. Get preprint from arXiv, Download from publisher.
P. Harjulehto and R. Hurri-Syrjänen: Embeddings into Orlicz spaces for functions from unbounded irregular domains, Complex Anal. Oper. Theory 13 (2019), no. 6, 2967-2992. 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.
P. Harjulehto and P. Hästö: Uniform convexity and associate spaces, Czechoslovak Math. J. 68 (2018), no.4, pp. 1011-1020. 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.
P. Harjulehto and R. Hurri-Syrjänen: Pointwise estimates to the modified Riesz potential, Manuscripta Math. 156 (2018), no. 3, 521-543. Get preprint from arXiv, 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), no. 2, article:22. 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 R. Klén: Generalized Orlicz spaces and related PDE, Nonlinear Anal. 143 (2016), 155-173. Preprint (PDF), Download from publisher.
P. Harjulehto and R. Hurri-Syrjänen: An embedding into an Orlicz space for $L^1_1$-functions from irregular domains, Proceedings of the international conference Complex Analysis and Dynamical Systems VI, part 1, 177-189, Contemp. Math., volume 653, Amer. Math. Soc., Providence, RI, 2015. Preprint (PDF), Download from publisher.
P. Harjulehto and R. Klén: Examples of fractals satisfying the quasihyperbolic boundary condition, Aust. J. Math. Anal. Appl. 12 (2015), Issue 1, Article 9, pp. 1-12. Preprint (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.
P. Harjulehto, R. Hurri-Syrjänen and J. Kapulainen: An embedding into an Orlicz space for irregular John domains, Comput. Methods Funct. Theory, 14 (2014), no. 2-3, 257-277, the special volume in honour of late Fred W. Gehring. Preprint (PDF), Download from journal.
J. Joutsenlahti, H. Sarikka, J. Kangas and P. Harjulehto: Matematiikan kirjallinen kielentäminen yliopiston matematiikan opetuksessa. (in english 'Languaging in math teaching in university level'), Proceedings of the annual conference of Finnish Mathematics and Science Education Research Association edited by M. Hähkiöniemi, H. Leppäaho, P. Nieminen and J. Viiri, Research Report Series of the Department of Teacher Education, University of Jyväskylä, 2013.
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), 676-681. Preprint (PDF), Download from journal.
P. Harjulehto, P. Hästö, V. Latvala and O. Toivanen, Critical variable exponent functionals in image restoration, Appl. Math. Lett. 26 (2013), 56-60. Preprint (PDF), Download from journal.
P. Harjulehto, R. Hurri-Syrjänen and A. V. Vähäkangas: On the (1,p)-Poincaré inequality, Illinois J. Math., 56 (2012), no. 3, 905-930. Preprint (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-uniformly convex, non-standard growth Laplacian, Complex Var. Elliptic Equ. 56 (2011), no. 7-9, 643-657. Preprint (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. Preprint (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.
P. Harjulehto, P. Hästö, U. V. Le and M. Nuortio: Overview of differential equations with non-standard growth, Nonlinear Anal. 72 (2010), 4551-4574. Preprint (PDF), Download from journal.
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).
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. 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.
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. Download from 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.
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.
P. Harjulehto and R. Hurri-Syrjänen: On a (q,p)-Poincaré inequality, J. Math. Anal. Appl 337 (2008), 61-68. Preprint (PDF), Download from journal.
P. Harjulehto, P. Hästö, M. Koskenoja, T. Lukkari and N. Marola: 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), Download from journal.
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 (2007), Article ID 32324, 18 pages, doi:10.1155/2007/32324. Download from journal.
P. Harjulehto, J. Kinnunen and T. Lukkari: Unbounded supersolutions of nonlinear equations with nonstandard growth, Bound. Value Probl. 2007 (2007), Article ID 48348, 20 pages, doi:10.1155/2007/48348. Download from journal.
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), Expanded version.
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. Harjulehto: Traces and Sobolev extension domains, Proc. Amer. Math. Soc., 134 (2006), 2373-2382. Download from journal.
P. Harjulehto, P. Hästö and M. Koskenoja: Hardy's inequality in a variable exponent Sobolev space, Georgian Math. J. 12 (2005), no. 3, 431--442. Preprint (PDF).
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, M. Koskenoja and S. Varonen: Variable Sobolev capacity and the assumptions on the exponent, Proceedings of The Orlicz Centenary Conference and Function Spaces VII, Volume II edited by H. Hudzik, J. Musielak and L. Skrzypczak, Banach Center Publ. 68 (2005), 51--59. Preprint (PDF).
P. Harjulehto and J. Kinnunen: Differentiation bases for Sobolev functions on metric spaces, Publ. Mat. 48 (2004), no. 2, 381--395. Preprint (PDF), Download from journal.
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 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 imbedding in variable exponent Sobolev spaces, Rev. Mat. Complut. 17 (2004), no. 1, 129--146. Preprint (PDF), Download from journal.
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).
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).
P. Harjulehto and P. Hästö: An overview of variable exponent Lebesgue and Sobolev spaces, Proceedings of the workshop on future trends in geometric function theory, RNC workshop Jyväskylä 2003 edited by D. Herron, Rep. Univ. Jyväskylä, Dept. Math. Stat. 92 (2003), 85--93. Preprint (PDF).
P. Harjulehto: Maximal inequality in (s,m)-uniform domains, Ann. Acad. Sci. Fenn. Math. 27 (2002), 291--306. Download from journal.
P. Harjulehto: Sobolev extension domains on metric spaces of homogeneous type, Real Anal. Exchange 27 (2001/2002), no. 2, 583--597. Download from journal.