Abstract Hardy spaces with variable exponents. (January 2018)

• Record Type: Journal Article
• Authors: Liu, Yin; Zhao, Jiman
• Is Part Of: Nonlinear analysis. Volume 167(2018)
• Page Start: 29
• Page End: 50
• Publication Date: 2018-01
• Subjects: 42B30 -- 42B35; Variable exponent Hardy spaces -- Atomic decomposition -- Molecular decomposition -- Bilinear operators; 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.2017.10.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we introduce the definition of abstract Hardy spaces with variable exponents via the atomic decomposition and molecular decomposition. We prove the continuity from our variable Hardy space H a t o p ( ⋅ ) into L p ( ⋅ ), where p ( ⋅ ) : R n → ( 0, 1 ], 0 < p − ⩽ p + ⩽ 1 . Moreover, we investigate the bilinear theory. Finally, we give an application of the abstract Hardy spaces with variable exponents.