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… 

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