Analysis related to all admissible type parameters in the Jacobi setting
Artikel i vetenskaplig tidskrift, 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

Spectral

Jacobi-Poisson kernel

Riesz transform

Författare

Adam Nowak

Polish Academy of Sciences

Peter Sjögren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Tomasz Z. Szarek

Polish Academy of Sciences

Constructive Approximation

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

Vol. 41 2 185-218

Fundament

Grundläggande vetenskaper

Ämneskategorier

Matematisk analys

DOI

10.1007/s00365-015-9275-5

Mer information

Senast uppdaterat

2023-02-01