International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 94768, 19 pages
doi:10.1155/IJMMS/2006/94768
Weyl transforms associated with the Riemann-Liouville operator
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.
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.