Three related problems of Bergman spaces of tube domains over symmetric cones

Bonami, Aline. "Three related problems of Bergman spaces of tube domains over symmetric cones." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.3-4 (2002): 183-197. <http://eudml.org/doc/252354>.

@article{Bonami2002,
abstract = {It has been known for a long time that the Szegö projection of tube domains over irreducible symmetric cones is unbounded in $L^\{p\}$ for $p \neq 2$. Indeed, this is a consequence of the fact that the characteristic function of a disc is not a Fourier multiplier, a fundamental theorem proved by C. Fefferman in the 70’s. The same problem, related to the Bergman projection, deserves a different approach. In this survey, based on joint work of the author with D. Békollé, G. Garrigós, M. Peloso and F. Ricci, we give partial results on the range of $p$ for which it is bounded. We also show that there are two equivalent problems, of independent interest. One is a generalization of Hardy inequality for holomorphic functions. The other one is the characterization of the boundary values of functions in the Bergman spaces in terms of an adapted Littlewood-Paley theory. This last point of view leads naturally to extend the study to spaces with mixed norm as well.},
author = {Bonami, Aline},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Whitney decomposition; Symmetric cone; Bergman projector; Littlewood-Paley; Hardy inequality; symmetric cone},
language = {eng},
month = {12},
number = {3-4},
pages = {183-197},
publisher = {Accademia Nazionale dei Lincei},
title = {Three related problems of Bergman spaces of tube domains over symmetric cones},
url = {http://eudml.org/doc/252354},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Bonami, Aline
TI - Three related problems of Bergman spaces of tube domains over symmetric cones
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/12//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 3-4
SP - 183
EP - 197
AB - It has been known for a long time that the Szegö projection of tube domains over irreducible symmetric cones is unbounded in $L^{p}$ for $p \neq 2$. Indeed, this is a consequence of the fact that the characteristic function of a disc is not a Fourier multiplier, a fundamental theorem proved by C. Fefferman in the 70’s. The same problem, related to the Bergman projection, deserves a different approach. In this survey, based on joint work of the author with D. Békollé, G. Garrigós, M. Peloso and F. Ricci, we give partial results on the range of $p$ for which it is bounded. We also show that there are two equivalent problems, of independent interest. One is a generalization of Hardy inequality for holomorphic functions. The other one is the characterization of the boundary values of functions in the Bergman spaces in terms of an adapted Littlewood-Paley theory. This last point of view leads naturally to extend the study to spaces with mixed norm as well.
LA - eng
KW - Whitney decomposition; Symmetric cone; Bergman projector; Littlewood-Paley; Hardy inequality; symmetric cone
UR - http://eudml.org/doc/252354
ER -