On the Calderón-Zygmund structure of Petermichl's kernel

Abstract

We show that Petermichl's dyadic operator P (Petermichl (2000) [8]) is a Calderón–Zygmund-type operator on an adequate metric normal space of homogeneous type. We also compare the maximal operators associated with truncations of the kernel and to the summability of the Haar series.