Parameterized Littlewood-Paley operators with variable kernels on Hardy spaces and weak Hardy spaces

TL;DR

This paper investigates the boundedness of parameterized Littlewood-Paley operators with variable kernels on Hardy and weak Hardy spaces using atomic decomposition theory.

Contribution

It introduces new boundedness results for these operators on Hardy and weak Hardy spaces, expanding understanding of their behavior in harmonic analysis.

Findings

Boundedness established for Hardy spaces

Boundedness established for weak Hardy spaces

Utilizes atomic decomposition theory

Abstract

In this paper, by using the atomic decomposition theory of Hardy space and weak Hardy space, we discuss the boundedness of parameterized Littlewood-Paley operator with variable kernel on these spaces.