On the boundedness of non-integer dimension Calder\'on-Zygmund Operators with antisymmetric kernels

TL;DR

This paper characterizes measures for which all non-integer dimension Calderón-Zygmund operators with antisymmetric kernels are bounded in L^2, using the Wolff energy as a key criterion.

Contribution

It provides a complete characterization of measure boundedness for a class of singular integral operators based on the Wolff energy.

Findings

Boundedness of operators characterized by Wolff energy

Applicable to non-integer dimension Calderón-Zygmund operators

Advances understanding of measure conditions for operator boundedness

Abstract

We characterize the non-atomic measures $\mu$ for which all Calder\'{o}n-Zygmund operators with antisymmetric kernels of a fixed non-integer dimension $s$ are bounded in $L^2(\mu)$ in terms of a positive quantity, the Wolff energy.