Fractional integration for Laguerre expansions
Authors: George Gasper, Krzysztof Stempak and Walter Trebels
Abstract:
A fractional integration theorem is derived within the framework of
Laguerre expansions. The method of proof consists of establishing an
asymptotic estimate for the kernel and then applying a method of
Hedberg [On certain convolution inequalities, Proc. Amer. Math.
Soc., 36 (1972), pp. 505 -- 510]. This result is combined with
sufficient $(p,p)$ multiplier criteria of Stempak and Trebels [On
weighted transplantation and multipliers for Laguerre expansions,
Math. Ann. 300 (1994), 203--219] to obtain sufficient $(p,q)$
multiplier criteria that are comparable with the necessary multiplier
criteria in Gasper and Trebels [Necessary multiplier conditions
for Laguerre expansions, Canad. J. Math., 43 (1991), 1228-1242;
II, SIAM J. Math. Anal. 25 (1994), 384--391].
This article will appear in
Methods and Applications of Analysis.
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