Illinois Journal of Mathematics

Higher order Riesz transforms for Laguerre expansions

Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa, and Alejandro Sanabria-García

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Abstract

In this paper, we investigate $L^p$-boundedness properties for the one-dimensional higher order Riesz transforms associated with Laguerre operators. We also prove that the $k$-th Riesz transform is a principal value singular integral operator (modulus a constant times of the function when $k$ is even). To establish our results, we exploit a new estimate connecting Riesz transforms in the Hermite and Laguerre settings in dimension one.

Article information

Source
Illinois J. Math., Volume 55, Number 1 (2011), 27-68.

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1355927026

Digital Object Identifier
doi:10.1215/ijm/1355927026

Mathematical Reviews number (MathSciNet)
MR3006678

Zentralblatt MATH identifier
1261.42041

Subjects
Primary: 42C05: Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
Secondary: 42C15: General harmonic expansions, frames

Citation

Betancor, Jorge J.; Fariña, Juan C.; Rodríguez-Mesa, Lourdes; Sanabria-García, Alejandro. Higher order Riesz transforms for Laguerre expansions. Illinois J. Math. 55 (2011), no. 1, 27--68. doi:10.1215/ijm/1355927026. https://projecteuclid.org/euclid.ijm/1355927026


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