An Algebra Containing the Two-Sided Convolution Operators

TL;DR

This paper introduces a new algebra of operators on stratified groups that includes two-sided convolution operators, expanding the scope of singular integral theory beyond classical Calderón-Zygmund frameworks.

Contribution

It defines an algebra containing right and left invariant Calderón-Zygmund operators that are pseudolocal and bounded on L^p spaces, extending classical singular integral theory.

Findings

Operators are pseudolocal and bounded on L^p

Algebra contains two-sided convolution operators

Extends singular integral theory beyond classical Calderón-Zygmund

Abstract

We present an intrinsically defined algebra of operators containing the right and left invariant Calder\'on-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on L^p (1<p<\infty). This algebra provides an example of an algebra of singular integrals that falls outside of the classical Calder\'on-Zygmund theory.