Riesz transforms for the Weinstein operator

Abstract

ABSTRACTIn this paper we study the Riesz transforms related to the Weinstein operators . We develop for a theory that runs parallel to the one for the Euclidean Riesz Transform. It is proved that the Riesz–Weinstein transform in coordinates , is actually a Calderón–Zygmund singular integral operator in the sense of the associated space of homogeneous type. Moreover, our Riesz–Weinstein transform can be written as a principal value.