On the boundedness of non-integer dimension Calderón-Zygmund Operators with antisymmetric kernels

Abstract

We characterize the non-atomic measures $\mu$ for which all Calderón-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.

20 pages. We have (rather deliberately) imported several definitions from the previous submission arXiv:1602.02821 with minimal changes so that the reader can compare similarities in the methods