Variable Exponent Besov–Morrey Spaces

被引：3
作者：
Alexandre Almeida
António Caetano
机构：
[1] University of Aveiro,Center for R&D in Mathematics and Applications, Department of Mathematics
来源：
Journal of Fourier Analysis and Applications | 2020年 / 26卷
关键词：
Variable exponents; Non-standard growth; Mixed Morrey-sequence spaces; Besov–Morrey spaces; Convolution inequalities; Maximal characterization; Atomic representation; Molecular representation; 46E35; 46E30; 42B25;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper we introduce Besov–Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.
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