Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions

Abstract

We present a new criterion for the weighted $L^p-L^q$ boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates for Laguerre and Hermite fractional integrals with a unified and simpler approach.

arXiv comment22 pages; new section added, corrected typos, new references added