International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 86238, 26 pages

Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators

C. Baccar, N. B. Hamadi, and L. T. Rachdi

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

Received 21 May 2005; Revised 27 September 2005; Accepted 20 October 2005

Copyright © 2006 C. Baccar et al. 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.


We define Riemann-Liouville transform α and its dual tα associated with two singular partial differential operators. We establish some results of harmonic analysis for the Fourier transform connected with α. Next, we prove inversion formulas for the operators α, tα and a Plancherel theorem for tα.