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

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.