\(L^p \) boundedness of Riesz transforms for orthogonal polynomials in a general context (Q2787152)
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scientific article; zbMATH DE number 6545409
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^p \) boundedness of Riesz transforms for orthogonal polynomials in a general context |
scientific article; zbMATH DE number 6545409 |
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24 February 2016
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orthogonal polynomials
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heat-diffusion semigroups
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Riesz functions
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\(L^p \) boundedness of Riesz transforms for orthogonal polynomials in a general context (English)
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In a well-known paper [J. Fourier Anal. Appl. 12, No. 6, 675--711 (2006; Zbl 1193.42065)], \textit{A. Nowak} and \textit{K. Stempak} presented a fairly general and unified approach to the theory of Riesz transforms and conjugacy in the setting of high-dimensional orthogonal expansions. The resulting scheme, emerging from observations furnished in numerous articles, allowed them to show the \(L^2\)-boundedness of the Riesz transforms in a rather effortless and general way.NEWLINENEWLINEIn the paper under review, the authors use this scheme to analyse sufficient conditions for the boundedness of these transforms on \(L^p,\) \(1<p<\infty\). Furthermore, they discuss a symmetrized version of these transforms.
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