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2018 Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions
Błażej Wróbel
Anal. PDE 11(3): 745-773 (2018). DOI: 10.2140/apde.2018.11.745

Abstract

An explicit Bellman function is used to prove a bilinear embedding theorem for operators associated with general multidimensional orthogonal expansions on product spaces. This is then applied to obtain Lp boundedness, 1<p<, of appropriate vectorial Riesz transforms, in particular in the case of Jacobi polynomials. Our estimates for the Lp norms of these Riesz transforms are both dimension-free and linear in max(p,p(p1)). The approach we present allows us to avoid the use of both differential forms and general spectral multipliers.

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Błażej Wróbel. "Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions." Anal. PDE 11 (3) 745 - 773, 2018. https://doi.org/10.2140/apde.2018.11.745

Information

Received: 23 January 2017; Revised: 31 July 2017; Accepted: 23 September 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 1380.42022
MathSciNet: MR3738261
Digital Object Identifier: 10.2140/apde.2018.11.745

Subjects:
Primary: 33C50, 42A50, 42C10

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 3 • 2018
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