Besov spaces and the boundedness of weighted Bergman projections over symmetric tube domains
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 f...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:2050 |
| Acceso en línea: | https://ddd.uab.cat/record/2050 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_49105_02 |
| Access Level: | acceso abierto |
| Palabra clave: | Bergman projection Jordan algebra Besov multipliers Boundary values |
| Sumario: | 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. |
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