On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded

References

[1] D. Cruz-Uribe, Interpolation of positive operators on variable Lebesgue spaces, Math. Inequal. Appl. 15 (2012), no. 3, 639–644. 10.7153/mia-15-56Search in Google Scholar

[2] D. Cruz-Uribe, A. Fiorenza and C. J. Neugebauer, The maximal function on variable L p spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), no. 1, 223–238. Search in Google Scholar

[3] D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces. Foundations and Harmonic Analysis, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Heidelberg, 2013. 10.1007/978-3-0348-0548-3Search in Google Scholar

[4] L. Diening, Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces, Bull. Sci. Math. 129 (2005), no. 8, 657–700. 10.1016/j.bulsci.2003.10.003Search in Google Scholar

[5] L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math. 2017, Springer, Heidelberg, 2011. 10.1007/978-3-642-18363-8Search in Google Scholar

[6] L. Diening, P. Hästö and A. Nekvinda, Open problems in variable Lebesgue and Sobolev spaces, FSDONA04 Proceedings, Czech Academy of Sciences, Milovy (2004), 38–58. Search in Google Scholar

[7] A. Fiorenza, A. Gogatishvili and T. Kopaliani, Estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces and applications, Izv. Nats. Akad. Nauk Armenii Mat. 49 (2014), no. 5, 11–22; translation in J. Contemp. Math. Anal. 49 (2014), no. 5, 232–240. 10.3103/S1068362314050045Search in Google Scholar

[8] A. Gogatishvili and T. Kopaliani, On the Rubio de Francia’s theorem in variable Lebesgue spaces, Bull. TICMI 18 (2014), no. 1, 3–10. Search in Google Scholar

[9] A. Gogatishvili and T. Kopaliani, Maximal multiplier operators in L p ⁢ ( ⋅ ) ⁢ ( ℝ n ) spaces, Bull. Sci. Math. 140 (2016), no. 4, 86–97. 10.1016/j.bulsci.2015.04.003Search in Google Scholar

[10] A. Y. Karlovich, Algebras of continuous Fourier multipliers on variable Lebesgue spaces, Mediterr. J. Math. 17 (2020), no. 4, Paper No. 102. 10.1007/s00009-020-01537-zSearch in Google Scholar

[11] A. Y. Karlovich and I. M. Spitkovsky, Pseudodifferential operators on variable Lebesgue spaces, Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, Oper. Theory Adv. Appl. 228, Birkhäuser/Springer, Basel (2013), 173–183. 10.1007/978-3-0348-0537-7_9Search in Google Scholar

[12] V. Kokilashvili, A. Meskhi, H. Rafeiro and S. Samko, Integral Operators in Non-Standard Function Spaces. Vol. 1. Variable Exponent Lebesgue and Amalgam Spaces, Oper. Theory Adv. Appl. 248, Birkhäuser/Springer, Cham, 2016. 10.1007/978-3-319-21015-5_1Search in Google Scholar

[13] A. K. Lerner, Some remarks on the Hardy–Littlewood maximal function on variable L p spaces, Math. Z. 251 (2005), no. 3, 509–521. 10.1007/s00209-005-0818-5Search in Google Scholar

[14] A. Nekvinda, Hardy–Littlewood maximal operator on L p ⁢ ( x ) ⁢ ( ℝ ) , Math. Inequal. Appl. 7 (2004), no. 2, 255–265. 10.7153/mia-07-28Search in Google Scholar

[15] A. Nekvinda, Maximal operator on variable Lebesgue spaces for almost monotone radial exponent, J. Math. Anal. Appl. 337 (2008), no. 2, 1345–1365. 10.1016/j.jmaa.2007.04.047Search in Google Scholar

[16] L. Pick and M. Růžička, An example of a space L p ⁢ ( x ) on which the Hardy–Littlewood maximal operator is not bounded, Expo. Math. 19 (2001), no. 4, 369–371. 10.1016/S0723-0869(01)80023-2Search in Google Scholar

[17] V. Rabinovich and S. Samko, Boundedness and Fredholmness of pseudodifferential operators in variable exponent spaces, Integral Equations Operator Theory 60 (2008), no. 4, 507–537. 10.1007/s00020-008-1566-9Search in Google Scholar