Singular integrals with variable kernels in dyadic settings

Abstract

In this paper we explore conditions on variable symbols with respect to Haar systems, defining Calderón-Zygmund type operators with respect to the dyadic metrics associated to the Haar bases.We show that Petermichl's dyadic kernel can be seen as a variable kernel singular integral and we extend it to dyadic systems built on spaces of homogeneous type.

17 pages