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Analysis related to all admissible type parameters in the Jacobi setting

Författare och institution:
Adam Nowak (-); Peter Sjögren (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Tomasz Z. Szarek (-)
Publicerad i:
Constructive approximation, 41 ( 2 ) s. 185-218
ISSN:
0176-4276
E-ISSN:
1432-0940
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2015
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Matematisk analys
Nyckelord:
Jacobi expansion, Jacobi-Poisson kernel, Maximal operator, Riesz transform, Square function, Spectral
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
213088
Posten skapad:
2015-02-25 09:01
Posten ändrad:
2016-07-13 12:40

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