# Fractional integration for Laguerre expansions

@article{Gasper1994FractionalIF, title={Fractional integration for Laguerre expansions}, author={George Gasper and Krzysztof Stempak and Walter Trebels}, journal={Methods and applications of analysis}, year={1994}, volume={2}, pages={67-75} }

The aim of this note is to provide a fractional integration theorem in the framework of Laguerre expansions. The method of proof consists of establishing an asymptotic estimate for the involved kernel and then applying a method of Hedberg [5]. We combine this result with sufficient (p, p) multiplier criteria of Stempak and Trebels [10]. The resulting sufficient (p, q) multiplier criteria are comparable with necessary ones of Gasper and Trebels [3]. Our notation is essentially that in [10]. Thus…

## 25 Citations

### Norm inequalities for fractional integrals of Laguerre and Hermite expansions

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Suppose the fractional integration operator I is generated by the sequence {(k + \)~} in the setting of Laguerre and Hermite expansions. Then, via projection formulas, the problem of the norm…

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Abstract We study negative powers of Laguerre differential operators in ${{\mathbb{R}}^{d}},\,d\,\ge \,1$ . For these operators we prove two-weight $[{{L}^{p}}\,-\,{{L}^{q}}$ estimates with ranges of…

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