International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 94768, 19 pages

Weyl transforms associated with the Riemann-Liouville operator

N. B. Hamadi and L. T. Rachdi

Department of Mathematics, Faculty of Sciences of Tunis, University Tunis, El Manar 2092, Tunis, Tunisia

Received 4 January 2006; Revised 21 June 2006; Accepted 8 August 2006

Copyright © 2006 N. B. Hamadi and L. T. Rachdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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