## Analysis & PDE

• Anal. PDE
• Volume 11, Number 3 (2018), 745-773.

### Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions

Błażej Wróbel

#### 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, 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 $max(p,p∕(p−1))$. The approach we present allows us to avoid the use of both differential forms and general spectral multipliers.

#### Article information

Source
Anal. PDE, Volume 11, Number 3 (2018), 745-773.

Dates
Revised: 31 July 2017
Accepted: 23 September 2017
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513774534

Digital Object Identifier
doi:10.2140/apde.2018.11.745

Mathematical Reviews number (MathSciNet)
MR3738261

Zentralblatt MATH identifier
1380.42022

#### Citation

Wróbel, Błażej. Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions. Anal. PDE 11 (2018), no. 3, 745--773. doi:10.2140/apde.2018.11.745. https://projecteuclid.org/euclid.apde/1513774534

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