Abstract

Abstract In this article, the authors establish the characterizations of a class of anisotropic Herz-type Hardy spaces with two variable exponents associated with a non-isotropic dilation on ℝ n {{\mathbb{R}}}^{n} in terms of molecular decompositions. Using the molecular decompositions, the authors obtain the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy space with two variable exponents.

Highlights

  • The theory of function spaces with variable exponents has rapidly made progress in the past 20 years since some elementary properties were established by Kováčik and Rákosník [1]

  • 2012, Almeida and Drihem [3] introduced the Herz spaces with two variable exponents and obtain the boundedness of some sublinear operators on those spaces

  • In 2003, Bownik [6] introduced the anisotropic Hardy spaces HAp ( n) associated with very general discrete groups of dilations. This formulation includes the classical isotropic Hardy space theory established by Fefferman and Stein [7] and the parabolic Hardy space theory established by Calderón and Torchinsky [8,9]

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Summary

Introduction

The theory of function spaces with variable exponents has rapidly made progress in the past 20 years since some elementary properties were established by Kováčik and Rákosník [1]. Wang and Liu [4] introduced the Herz-type Hardy spaces with variable exponents HKpα(,⋅q) In 2003, Bownik [6] introduced the anisotropic Hardy spaces HAp ( n) associated with very general discrete groups of dilations. In 2008, Ding et al [10] introduced the anisotropic Herz-type Hardy spaces HKpα,q (A; n) and HKpα,q (A; n) and established their atomic and molecular decompositions. In 2018, Zhao and Zhou [11] introduced the variable anisotropic Herz-type Hardy spaces HKpα(,⋅q) (A; n) and HKpα,(q⋅) (A; n) and established their atomic and molecular decompositions. Using these decompositions, they gave some applications. HKpα((⋅⋅)),q (A; n) and HKpα((⋅⋅)),q (A; n) and established their atomic decomposition and some applications

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