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Analysis related to all admissible type parameters in the Jacobi setting

Adam Nowak ; Peter Sjögren (Institutionen för matematiska vetenskaper, matematik) ; Tomasz Z. Szarek
Constructive approximation (0176-4276). Vol. 41 (2015), 2, p. 185-218.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Jacobi expansion, Jacobi-Poisson kernel, Maximal operator, Riesz transform, Square function, Spectral



Denna post skapades 2015-02-25. Senast ändrad 2016-07-13.
CPL Pubid: 213088

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys

Chalmers infrastruktur