Molecular Characterizations and Dualities of Variable Exponent Hardy Spaces Associated with Operators

2015/12/18 by Yang, Dachun, Zhuo, Ciqiang
#35K08 #47D03 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42B35 #Secondary 42B30

paper · doi:10.48550/arxiv.1512.05950

Abstract

Let L be a linear operator on L²(\mathbb Rⁿ) generating an analytic semigroup \e^-tL\_t≥0 with kernels having pointwise upper bounds and p(⋅): \mathbb Rⁿ→(0,1] be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the authors introduce the variable exponent Hardy space associated with the operator L, denoted by H_L^p(⋅)(\mathbb Rⁿ), and the BMO-type space BMO_p(⋅),L(\mathbb Rⁿ). By means of tent spaces with variable exponents, the authors then establish the molecular characterization of H_L^p(⋅)(\mathbb Rⁿ) and a duality theorem between such a Hardy space and a BMO-type space. As applications, the authors study the boundedness of the fractional integral on these Hardy spaces and the coincidence between H_L^p(⋅)(\mathbb Rⁿ) and the variable exponent Hardy spaces H^p(⋅)(\mathbb Rⁿ).

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