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Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions

✍ Scribed by Piotr Graczyk; Jean-J. Loeb; Iris A. López P.; Adam Nowak; Wilfredo O. Urbina R.

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 244 KB
Volume: 84
Category: Article
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2004.09.003

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✦ Synopsis

We study different Sobolev spaces associated with multidimensional Laguerre expansions. To do this we establish an analogue of P.A. Meyer's multiplier theorem, prove some transference results between higher order Riesz-Hermite and Riesz-Laguerre transforms, and introduce fractional derivatives and integrals corresponding to the Laguerre setting. Hypercontractivity of the Laguerre semigroups and Calderón's reproduction formula are also discussed.