Taiwanese Journal of Mathematics

DIMENSION FREE $L^P$ ESTIMATES FOR RIESZ TRANSFORMS ASSOCIATED WITH LAGUERRE FUNCTION EXPANSIONS OF HERMITE TYPE

Błażej Wróbel and Krzysztof Stempak

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 17, Number 1 (2013), 63-81.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705876

Digital Object Identifier
doi:10.11650/tjm.17.2013.1939

Mathematical Reviews number (MathSciNet)
MR3028858

Zentralblatt MATH identifier
1285.42023

Subjects
Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Laguerre expansions Riesz transforms dimension free $L^p$ estimates $g$-functions

Citation

Wróbel, Błażej; Stempak, Krzysztof. DIMENSION FREE $L^P$ ESTIMATES FOR RIESZ TRANSFORMS ASSOCIATED WITH LAGUERRE FUNCTION EXPANSIONS OF HERMITE TYPE. Taiwanese J. Math. 17 (2013), no. 1, 63--81. doi:10.11650/tjm.17.2013.1939. https://projecteuclid.org/euclid.twjm/1499705876


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