On the A_2 inequality for Calderon-Zygmund Operators

TL;DR

This paper proves that Calderon-Zygmund operators satisfy the linear A_2 bound, confirming a key inequality in weighted harmonic analysis using a novel combination of distributional inequalities, Haar functions, and stopping times.

Contribution

The paper establishes the A_2 inequality for Calderon-Zygmund operators with a new proof approach involving distributional inequalities and adapted Haar functions.

Findings

Calderon-Zygmund operators satisfy the linear A_2 bound.

The proof uses distributional inequalities and adapted Haar functions.

The approach simplifies existing proofs of the A_2 inequality.

Abstract

We prove that for a Calderon-Zygmund operator and weight w\in A_2, that it satisfies the linear in A2 bound due to Hytonen. Our proof will appeal to a distributional inequality used by several authors, adapted Haar functions, and standard stopping times.