Weighted local Hardy spaces with variable exponents

TL;DR

This paper introduces local weighted Hardy spaces with variable exponents, establishing atomic decompositions and boundedness of operators, advancing harmonic analysis tools for variable exponent function spaces.

Contribution

It defines local weighted Hardy spaces with variable exponents and proves atomic decomposition, boundedness of singular integrals, and wavelet characterizations.

Findings

Atomic decomposition for functions in variable exponent Lebesgue spaces

Boundedness of singular integral operators on these spaces

Littlewood--Paley and wavelet characterizations

Abstract

This paper defines local weighted Hardy spaces with variable exponent. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the functions in the Lebesgue spaces with exponentially decaying exponent. As an application, we obtain the boundedness of singular integral operators, the Littlewood--Paley characterization and wavelet decomposition.