Weinstein multipliers of Laplace transform type

Abstract

ABSTRACTIn this paper, we establish that Weinstein multipliers of Laplace transform type are Calderön–Zygmund operators in the sense of the associated space of homogeneous type, thus their mapping properties follow from the general theory. As an application, we deduce the -boundedness properties for the imaginary powers of the Weinstein operators . Finally we analyse the negative powers of and we give another result of boundedness of type for this operator.