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2013 DIMENSION FREE $L^P$ ESTIMATES FOR RIESZ TRANSFORMS ASSOCIATED WITH LAGUERRE FUNCTION EXPANSIONS OF HERMITE TYPE
Błażej Wróbel, Krzysztof Stempak
Taiwanese J. Math. 17(1): 63-81 (2013). DOI: 10.11650/tjm.17.2013.1939

Abstract

We prove dimension free $L^p$ estimates for Riesz transforms associated with multi-dimensional Laguerre function expansions of Hermite type. The range of the admissible Laguerre type multi-index $\alpha$ in these estimates depends on $p \in (1,\infty)$; for $1 \lt p \le 2$ this range is almost optimal. The proof is based on suitably defined square functions with Poisson and modified Poisson semigroups involved.

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Błażej Wróbel. Krzysztof Stempak. "DIMENSION FREE $L^P$ ESTIMATES FOR RIESZ TRANSFORMS ASSOCIATED WITH LAGUERRE FUNCTION EXPANSIONS OF HERMITE TYPE." Taiwanese J. Math. 17 (1) 63 - 81, 2013. https://doi.org/10.11650/tjm.17.2013.1939

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1285.42023
MathSciNet: MR3028858
Digital Object Identifier: 10.11650/tjm.17.2013.1939

Subjects:
Primary: 42C10
Secondary: 42B20, 42B25

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 1 • 2013
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