On pointwise estimates involving sparse operators

TL;DR

This paper presents an elementary alternative method to establish pointwise domination of Calderón-Zygmund operators by sparse operators, extending to certain non-integral singular operators.

Contribution

It introduces a simpler, more elementary approach to recent sparse domination results, applicable to a broader class of singular operators.

Findings

Successfully reproduces recent sparse domination results

Extends the approach to non-integral singular operators

Provides a more accessible proof technique

Abstract

We obtain an alternative approach to recent results by M. Lacey \cite{La} and T. Hyt\"onen {\it et al.} \cite{HRT} about a pointwise domination of $\omega$-Calder\'on-Zygmund operators by sparse operators. This approach is rather elementary and it also works for a class of non-integral singular operators.