Calderón‐Zygmund operators with non‐diagonal singularity

Abstract

ABSTRACT. In this paper, we introduce a class of singular integral operators which generalize Calderón-Zygmund operators to the more general case, where the set of singular points of the kernel need not to be the diagonal, but instead, it can be a general hyper curve. We show that such operators have similar properties as ordinary Calderón-Zygmund operators. In particular, we prove that they are of weak-type (1, 1) and strong type (p, p) for 1 < p < ∞.