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：
暂无
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.
引用
收藏
相关论文
共 77 条
[1]  
Acerbi E(2001)Regularity results for a class of functionals with nonstandard growth Arch. Ration. Mech. Anal. 156 121-140
[2]  
Mingione G(2016)On Nonlinear Anal. 135 97-119
[3]  
Almeida A(2016)-microlocal spaces with all exponents variable J. Funct. Anal. 270 1888-1921
[4]  
Caetano A(2010)Atomic and molecular decompositions in variable exponent J. Funct. Anal. 258 1628-1655
[5]  
Almeida A(2008)-microlocal spaces and applications Georgian Math. J. 15 195-208
[6]  
Caetano A(1964)Besov spaces with variable smoothness and integrability Ann. Sc. Norm. Super. Pisa 18 137-160
[7]  
Almeida A(2006)Maximal and potential operators in variable exponent Morrey spaces SIAM J. Appl. Math. 66 1383-1406
[8]  
Hästö P(2009)Proprietà di una famiglia di spazi funzioni J. Funct. Anal. 256 1731-1768
[9]  
Almeida A(2015)Variable exponent, linear growth functionals in image restoration Ann. Funct. Anal. 6 255-288
[10]  
Hasanov J(2015)Function spaces of variable smoothness and integrability Funct. Approx. Comment. Math. 52 193-221
12345678