A class of singular integrals associated with Zygmund dilations

TL;DR

This paper introduces a new class of multi-parameter singular integral operators linked to Zygmund dilations and proves their boundedness on L^p spaces, extending previous results by Ricci--Stein and Nagel--Wainger.

Contribution

It defines a novel class of singular integrals associated with Zygmund dilations and establishes their boundedness on L^p spaces, broadening the scope of prior work.

Findings

Proved boundedness of the new class of operators on L^p spaces

Extended previous results by Ricci--Stein and Nagel--Wainger

Introduced a framework for multi-parameter singular integrals

Abstract

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for these operators on $L^p, 1<p<\infty$, which covers those studied by Ricci--Stein \cite{RS} and Nagel--Wainger \cite{NW}