ABSTRACT
In 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.
Acknowledgements
I am grateful to Professor Néjib Ben Salem for suggesting the topic and for continuous encouragement to the study.
Disclosure statement
No potential conflict of interest was reported by the author.