WEIGHTED NORM INEQUALITIES FOR FRACTIONAL INTEGRALS WITH AN APPLICATION TO MEAN CONVERGENCE OF LAGUERRE SERIES

We prove norm inequalities with exponential weights for the Riemann-Li ouville fractional integral. As an application, we show for certain fu nctions that their Laguerre expansions will converge in the L-p norm f or some p outside the standard range of (4/3, 3). (C) 1997 Academic Pr ess.