Elementary proofs of one weight norm inequalities for fractional integral operators and commutators

TL;DR

This paper presents new, straightforward proofs for one-weight norm inequalities related to fractional integral operators and their commutators, utilizing dyadic grids and sparse operators.

Contribution

It introduces elementary proof techniques for these inequalities, simplifying previous complex methods and leveraging tools from the A2 conjecture proof.

Findings

Simplified proofs for fractional integral operator inequalities

Extension of sparse operator techniques to commutators

Enhanced understanding of weighted inequalities

Abstract

We give new and elementary proofs of one weight norm inequalities for fractional integral operators and commutators. Our proofs are based on the machinery of dyadic grids and sparse operators used in the proof of the A2 conjecture.