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Besov spaces and the boundedness of weighted Bergman projections over symmetric tube domains
Debertol, Daniele

Data: 2005
Resum: We extend the analysis of weighted Bergman spaces Ap;q/s on symmetric tube domains, contained in [2], to the case where the weights are positive powers [formula] of the principal minors [Delta]1,. . . ,[Delta]r on the symmetric cone [omega]. We discuss the realization of the boundary distributions of functions in Ap;q/s in terms of Besov-type spaces Bp;q/s adapted to the structure of the cone. We give a necessary and a sufficient condition on the values of p, q and s for which this identification between Ap;q/s and Bp;q/s holds. We also present a continuous version of thesse latter spaces which is new even for the case s1 = . . . = s1 considered in [2]. We use these results to discuss multipliers between Besov spaces and the boundedness of the weighted Bergman projection Ps: Lp;q/s --> Ap;q/s. The situation in the rank two case is specifically dealt with.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Bergman projection ; Jordan algebra ; Besov multipliers ; Boundary values
Publicat a: Publicacions matematiques, V. 49 N. 1 (2005) , p. 21-72, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_49105_02

52 p, 378.1 KB

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