Weyl transforms associated with the Riemann-Liouville operator

Abstract

For the Riemann-Liouville transformℛα, α∈ℝ+,associated with singular partial differential operators, we define and study the Weyl transformsWσconnected withℛα, whereσis a symbol inSm,m∈ℝ. We give criteria in terms ofσfor boundedness and compactness of the transformWσ.