International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 17, Article ID 94768, 19 pages
doi:10.1155/IJMMS/2006/94768

Weyl transforms associated with the Riemann-Liouville operator

Abstract

For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.