Boundedness of maximal operators and Sobolevʼs inequality on Musielak–Orlicz–Morrey spaces

By F. Maeda, Y. Mizuta, T. Ohno, Tetsu Shimomura. 2013

120 citations recorded by the source corpus.

Abstract Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator on Musielak–Orlicz–Morrey spaces. As an application of the boundedness of the maximal operator, we establish a generalization of Sobolevʼs inequality for general potentials of functions in Musielak–Orlicz–Morrey spaces.

Subfields: Applied Mathematics

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In Applied Mathematics

Citations in the corpus

Hölder regularity of quasiminimizers under generalized growth conditions (2017, methodology): “This approach is inspired by our Japanese colleagues [27], although our assumptions are more general than theirs, cf.”
Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space (2017, methodology): “e is the interplay between types of continuity with respect to each of the variables separately. Besides our condition (6) (suﬃcient for (M) via Lemma 3.2), we refer to the approaches of [27, 28] and [31, 32], where the authors deal with the modular function of the form M(x,ξ) = |ξ|φ(x,|ξ|). We proc”
Extrapolation and interpolation in generalized Orlicz spaces (2018, background): “Recently, however, attention has shifted to studying these problems in more generality: see [41, 42, 47].”
The maximal operator on generalized Orlicz spaces (2015, background): “Condition (Φ5) in [10, 11, 16] is essentially the same as (A1) in this paper.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Let us refer to the approaches of [117, 120] and [150, 151], where the authors deal with the isotropic modular function of the form M(x, ξ) = |ξ|φ(x, |ξ|).”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “See Mizuta, Nakai, Ohno and Shimomura [123, 125] and Maeda, Mizuta, Ohno and Shimomura [115].”
Non-autonomous functionals, borderline cases and related function classes (2016, background): “Both functionals give a relevant example of energy underlying a so-called Musielak-Orlicz space [24, 46, 56] and this point is briefly described in Section 2.”