WEYL TRANSFORMS ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR

Abstract

Using the harmonic analysis associated with the spherical mean operator ℛ, we define and study the Weyl transforms W σ associated with ℛ where σ is a symbol in S m , m ∈ ℝ, and we give criteria in terms of σ to obtain the boundedness and compactness of the transform W σ .