Maximal function characterizations of variable Hardy spaces associated with non-negative self-adjoint operators satisfying Gaussian estimates. (August 2016)

• Record Type: Journal Article
• Authors: Zhuo, Ciqiang; Yang, Dachun
• Is Part Of: Nonlinear analysis. Volume 141(2016)
• Page Start: 16
• Page End: 42
• Publication Date: 2016-08
• Subjects: primary 42B25 -- secondary 42B30 42B35 35K08; Non-negative self-adjoint operator -- Gaussian upper bound estimate -- Variable exponent Hardy space -- Atom -- Non-tangential maximal function -- Radial maximal function; 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.2016.03.025
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let p ( ⋅ ) : R n → ( 0, 1 ] be a variable exponent function satisfying the globally log -Hölder continuous condition and L a non-negative self-adjoint operator on L 2 ( R n ) whose heat kernels satisfying the Gaussian upper bound estimates. Let H L p ( ⋅ ) ( R n ) be the variable exponent Hardy space defined via the Lusin area function associated with the heat kernels { e − t 2 L } t ∈ ( 0, ∞ ) . In this article, the authors first establish the atomic characterization of H L p ( ⋅ ) ( R n ) ; using this, the authors then obtain its non-tangential maximal function characterization which, when p ( ⋅ ) is a constant in ( 0, 1 ], coincides with a recent result by L. Song and L. Yan (2016) and further induces the radial maximal function characterization of H L p ( ⋅ ) ( R n ) under an additional assumption that the heat kernels of L have the Hölder regularity.