Singular integrals with product kernels associated with mixed homogeneities and Hardy spaces

TL;DR

This paper investigates non-standard singular integrals with mixed homogeneities, establishing their boundedness on Hardy spaces, extending classical harmonic analysis results to more complex kernel structures.

Contribution

It introduces new non-standard convolution singular integrals with mixed homogeneities and proves their boundedness on Hardy spaces, expanding the scope of singular integral theory.

Findings

Boundedness of these singular integrals on Hardy spaces

Extension of classical results to mixed homogeneity kernels

New techniques for analyzing non-standard convolution operators

Abstract

This paper is motivated by Phong and Stein's paper on non-standard singular integrals with mixed homogeneities. Our purpose is to study these new non-standard convolution singular integrals and establish the boundedness of these singular integrals on the Hardy spaces.