Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions

Mathematics – Classical Analysis and ODEs

Scientific paper

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22 pages; new section added, corrected typos, new references added

Scientific paper

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.

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