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

摘要

We define Riemann-Liouville transform?αand its dualt?αassociated with two singular partialdifferential operators. We establish some results of harmonicanalysis for the Fourier transform connected with?α. Next, we prove inversion formulas for theoperators?α,t?αand a Plancherel theorem fort?α.