Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent. (September 2020)

• Record Type: Journal Article
• Authors: Izuki, Mitsuo; Nogayama, Toru; Noi, Takahiro; Sawano, Yoshihiro
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 42B35 -- 42C40; Variable exponent -- Wavelet -- Local Muckenhoupt weight -- Modular inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111930
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular inequalities to hold. One big achievement is that the weights with exponential growth can be handled in the framework of variable exponents.