Analysis related to all admissible type parameters in the Jacobi setting
Journal article, 2015

We derive an integral representation for the Jacobi-Poisson kernel valid for all admissible type parameters a and b in the context of Jacobi expansions. This enables us to develop a technique for proving standard estimates in the Jacobi setting, which works for all possible a and b. As a consequence, we can prove that several fundamental operators in the harmonic analysis of Jacobi expansions are (vector-valued) Calderón-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory. The new Jacobi-Poisson kernel representation also leads to sharp estimates of this kernel. The paper generalizes methods and results existing in the literature, but valid or justified only for a restricted range of a and b.

Square function

Jacobi-Poisson kernel

Spectral

Maximal operator

Jacobi expansion

Riesz transform

Author

Adam Nowak

Polish Academy of Sciences

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Tomasz Z. Szarek

Polish Academy of Sciences

Constructive Approximation

0176-4276 (ISSN) 1432-0940 (eISSN)

Vol. 41 2 185-218

Roots

Basic sciences

Subject Categories

Mathematical Analysis

DOI

10.1007/s00365-015-9275-5

More information

Latest update

10/30/2018