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
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 boundedness, , of appropriate vectorial Riesz transforms, in particular in the case of Jacobi polynomials. Our estimates for the norms of these Riesz transforms are both dimension-free and linear in . The approach we present allows us to avoid the use of both differential forms and general spectral multipliers.
Anal. PDE, Volume 11, Number 3 (2018), 745-773.
Received: 23 January 2017
Revised: 31 July 2017
Accepted: 23 September 2017
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42A50: Conjugate functions, conjugate series, singular integrals 33C50: Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
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