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L2-Theory of Riesz Transforms for Orthogonal Expansions

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Abstract

We propose a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions. The scheme is supported by numerous examples concerning, in particular, the classical orthogonal expansions in Hermite, Laguerre, and Jacobi polynomials. A general case of expansions associated to a regular or singular Sturm-Liouville problem is also discussed.

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  1. Instytut Matematyki i Informatyki, Politechnika Wrocławska, Wyb. Wyspianskiego 27, 50–370, Wrocław, Poland

    Adam Nowak & Krzysztof Stempak

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  1. Adam Nowak
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  2. Krzysztof Stempak
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Correspondence to Adam Nowak or Krzysztof Stempak.

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Nowak, A., Stempak, K. L2-Theory of Riesz Transforms for Orthogonal Expansions. J Fourier Anal Appl 12, 675–711 (2006). https://doi.org/10.1007/s00041-006-6034-9

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  • DOI: https://doi.org/10.1007/s00041-006-6034-9

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