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.

Jacobi expansion

Maximal operator

Square function


Jacobi-Poisson kernel

Riesz transform


Adam Nowak

Polish Academy of Sciences

Peter Sjögren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Tomasz Z. Szarek

Polish Academy of Sciences

Constructive Approximation

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

Vol. 41 2 185-218


Basic sciences

Subject Categories

Mathematical Analysis



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