Categories of results in variable Lebesgue spaces theory

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1. Acerbi, E. and Mingione, G.. Regularity results for electrorheological fluids: the stationary case. C. R. Math. Acad. Sci. Paris, 334(9):817–822, 2002. Zbl1017.76098MR1905047DOI10.1016/S1631-073X(02)02337-3
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7. Ambrosio, L., Fusco, N., and Pallara, D.. Functions of bounded variation and free discontinu- ity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 2000. Zbl0957.49001MR1857292
8. Anatriello, G., Chill, R., and Fiorenza, A.. Identification of fully measurable grand Lebesgue spaces. J. Funct. Spaces, pages 3, Art. ID 3129186, 2017. Zbl1386.46029MR3713073DOI10.1155/2017/3129186
9. Anatriello, G., Fiorenza, A., and Vincenzi, G.. Banach function norms via Cauchy polynomials and applications. Internat. J. Math., 26(10), pages 20, 1550083, 2015. Zbl1345.46003MR3401968DOI10.1142/S0129167X15500834
10. Antontsev, S. N. and Shmarev, S. I.. Evolution PDEs with nonstandard growth conditions, volume 4 of Atlantis Studies in Differential Equations. Existence, uniqueness, localization, blow-up. Atlantis Press, Paris, 2015. Zbl1410.35001MR3328376DOI10.2991/978-94-6239-112-3
11. Antontsev, S. N. and Shmarev, S. I.. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions. Nonlinear Anal., 60(3):515–545, 2005. Zbl1066.35045MR2103951DOI10.1016/j.na.2004.09.026
12. Baroni, P., Colombo, M., and Mingione, G.. Nonautonomous functionals, borderline cases and related function classes. Algebra i Analiz, 27(3):6–50, 2015. Zbl1335.49057MR3570955DOI10.1090/spmj/1392
13. Baroni, P., Colombo, M., and Mingione, G.. Harnack inequalities for double phase functionals. Nonlinear Anal., 121:206–222, 2015. Zbl1321.49059MR3348922DOI10.1016/j.na.2014.11.001
14. Baruah, D., Harjulehto, P., and Hästö, P.. Capacities in generalized Orlicz spaces. J. Funct. Spaces, pages 10, Art. ID 8459874, 2018. Zbl1409.46024MR3864628DOI10.1155/2018/8459874
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18. Brezis, H.. Analyse fonctionnelle. Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master’s Degree]. Masson, Paris, 1983. Théorie et applications.[Theory and applications]. MR697382
19. Brezis, H.. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Zbl1220.46002MR2759829
20. Capone, C., Cruz-Uribe, D., and Fiorenza, A.. The fractional maximal operator and fractional integrals on variable $L^p$ spaces. Rev. Mat. Iberoam., 23(3):743–770, 2007. Zbl1213.42063MR2414490DOI10.4171/RMI/511
21. Castillo, R. E. and Rafeiro, H.. An introductory course in Lebesgue spaces. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer, [Cham], 2016. Zbl1352.46003MR3497415DOI10.1007/978-3-319-30034-4
22. Çekiç, B., Kalinin, A. V., Mashiyev, R. A., and Avci, M.. $l^{p(x)}(\mathrm{\Omega })$-estimates for vector fields and some applications to magnetostatics problems. J. Math. Anal. Appl., 389(2):838–851, 2012. Zbl1234.35192MR2879262DOI10.1016/j.jmaa.2011.12.029
23. Colombo, M. and Mingione, G.. Bounded minimisers of double phase variational integrals. Arch. Ration. Mech. Anal., 218(1):219–273, 2015. Zbl1325.49042MR3360738DOI10.1007/s00205-015-0859-9
24. Cruz-Uribe, D., Diening, L., and Fiorenza, A.. A new proof of the boundedness of maximal operators on variable Lebesgue spaces. Boll. Unione Mat. Ital. (9), 2(1):151–173, 2009. Zbl1207.42011MR2493649
25. Cruz-Uribe, D., Di Fratta, G., and Fiorenza, A.. Modular inequalities for the maximal operator in variable Lebesgue spaces. Nonlinear Anal., 177(part A):299–311, 2018. Zbl1412.42047MR3865200DOI10.1016/j.na.2018.01.007
26. Cruz-Uribe, D. and Fiorenza, A.. Approximate identities in variable $L^p$ spaces. Math. Nachr., 280(3):256–270, 2007. Zbl1178.42022MR2292148DOI10.1002/mana.200410479
27. Cruz-Uribe, D. V. and Fiorenza, A.. Variable Lebesgue spaces. Applied and Numerical Harmonic Analysis. Birkhäuser/Springer, Heidelberg, 2013. Foundations and harmonic analysis. Zbl1268.46002MR3026953DOI10.1007/978-3-0348-0548-3
28. Cruz-Uribe, D., Fiorenza, A., Martell,, J. M. and Pérez, C.. The boundedness of classical operators on variable $L^p$ spaces. Ann. Acad. Sci. Fenn. Math., 31(1):239–264, 2006. Zbl1100.42012MR2210118
29. Cruz-Uribe, D., Fiorenza,, A. and Neugebauer, C. J.. The maximal function on variable $L^p$ spaces. Ann. Acad. Sci. Fenn. Math., 28(1):223–238, 2003. See also errata [30]. Zbl1037.42023MR1976842
30. Cruz-Urib, D.e, Fiorenza,, A. and Neugebauer, C. J.. Corrections to: “The maximal function on variable $L^p$ spaces” [Ann. Acad. Sci. Fenn. Math. 28 (2003), no. 1, 223–238; ]. Ann. Acad. Sci. Fenn. Math., 29(1):247–249, 2004. Zbl1064.42500MR2041952
31. Cruz-Uribe, D. V., Fiorenza, A., Ruzhansky,, M. and Wirth, J.. Lebesgu, Variablee spaces and hyperbolic systems. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer, Basel, 2014. Selected lecture notes from the Advanced Courses on Approximation Theory and Fourier Analysis held at the Centre de Recerca Matemàtica, Barcelona, November 7–11, 2011, Edited by Sergey Tikhonov. MR3364250
32. Cruz-Uribe, D. and Hästö, P.. Extrapolation and interpolation in generalized Orlicz spaces. Trans. Amer. Math. Soc., 370(6):4323–4349, 2018. Zbl1391.46037MR3811530DOI10.1090/tran/7155
33. Cruz-Uribe, D., Martell,, J. M. and Pérez, C.. Weights, extrapolation and the theory of Rubio de Francia, volume 215 of Operator Theory: Advances and Applications. Birkhäuser/Springer, [Cham], 2011. Zbl1234.46003MR2797562DOI10.1007/978-3-0348-0072-3
34. D’Aristotile, A. M. and Fiorenza, A.. A topology on inequalities. Electron. J. Differential Equations, pages 22, No. 85, 2006. Zbl1124.46020MR2240833
35. DiBenedetto, E.. Real analysis. Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser Boston, Inc., Boston, MA, 2002. MR1897317DOI10.1007/978-1-4612-0117-5
36. Diening, L.. Maximal function on generalized Lebesgue spaces $L^{p(\cdot )}$. Math. Inequal. Appl., 7(2):245–253, 2004. Zbl1071.42014MR2057643DOI10.7153/mia-07-27
37. Diening, L.. Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces. Bull. Sci. Math., 129(8):657–700, 2005. Zbl1096.46013MR2166733DOI10.1016/j.bulsci.2003.10.003
38. Diening, L.. Lebesgue and Sobolev Spaces with Variable Exponent. Habilitation, Universität Freiburg, 2007. 
39. Diening, L., Harjulehto, P., Hästö,, P. and Růžička, M.. Lebesgue and Sobolev spaces with variable exponents, volume 2017 of Lecture Notes in Mathematics. Springer, Heidelberg, 2011. Zbl1222.46002MR2790542DOI10.1007/978-3-642-18363-8
40. Diening, L. and Růžička, M.. Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(\cdot )}$ and problems related to fluid dynamics. J. Reine Angew. Math., 563:197–220, 2003. Zbl1072.76071MR2009242DOI10.1515/crll.2003.081
41. Diening, L. and Růžička, M.. Integral operators on the halfspace in generalized Lebesgue spaces $L^{p(\cdot )}$. I. J. Math. Anal. Appl., 298(2):559–571, 2004. Zbl1128.47044MR2086975DOI10.1016/j.jmaa.2004.05.048
42. Diening, L. and Růžička, M.. Integral operators on the halfspace in generalized Lebesgue spaces $L^{p(\cdot )}$. II. J. Math. Anal. Appl., 298(2):572–588, 2004. Zbl1128.47044MR2086976DOI10.1016/j.jmaa.2004.05.049
43. Diening, L. and Růžička, M.. Non-Newtonian fluids and function spaces. In NAFSA 8— Nonlinear analysis, function spaces and applications. Vol. 8, pages 94–143. Czech. Acad. Sci., Prague, 2007. Zbl1289.35104MR2657118
44. Diening, L., Harjulehto, P., Hästö, P., Mizuta,, Y. and Shimomura, T.. Maximal functions in variable exponent spaces: limiting cases of the exponent. Ann. Acad. Sci. Fenn. Math., 34(2):503–522, 2009. Zbl1180.42010MR2553809
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62. Fiorenza, A.. A local estimate for the maximal function in Lebesgue spaces with EXP-type exponents. J. Funct. Spaces, pages 5, Art. ID 581064, 2015. Zbl1327.42021MR3352135DOI10.1155/2015/581064
63. Fiorenza, A., Kokilashvili,, V. and Meskhi, A.. Hardy-Littlewood maximal operator in weighted grand variable exponent Lebesgue space. Mediterr. J. Math., 14(3), pages 20, Art. 118, 2017. Zbl1375.26014MR3635958DOI10.1007/s00009-017-0921-y
64. Fiorenza, A. and Krbec, M.. A note on noneffective weights in variable Lebesgue spaces. J. Funct. Spaces Appl., pages 5, Art. ID 853232, 2012. Zbl1239.46023MR2873706DOI10.1155/2012/853232
65. Fiorenza, A. and Rakotoson, J. M.. Relative rearrangement and Lebesgue spaces $L^{p(\cdot )}$ with variable exponent. J. Math. Pures Appl. (9), 88(6):506–521, 2007. Zbl1137.46016MR2373739DOI10.1016/j.matpur.2007.09.004
66. Fiorenza, A., Rakotoson,, J. M. and Sbordone, C.. Variable exponents and grand Lebesgue spaces: some optimal results. Commun. Contemp. Math., 17(6):1550023, 14, 2015. Zbl1351.46024MR3485874DOI10.1142/S0219199715500236
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