Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones

Autor: Sami Ali, Obaid.B. A. A, Ahmed Sufyan Abakar, Shawgy Hussein
Jazyk: angličtina
Rok vydání: 2022
Předmět:
ISSN: 2348-5736
DOI: 10.5281/zenodo.7157246
Popis: The Szego projection of tube domains over irreducible symmetric cones is unbounded in . 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. Bekolle , G .Garrigos , M . Peloso and F . Ricci , we give partial results on the range of 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. Keywords: Whitney decomposition; Symmetric cone; Bergman projector; Littlewood – Paley; Hardy inequality. Title: Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones Author: Sami Ali, Obaid.B. A. A, Ahmed Sufyan Abakar, Shawgy Hussein International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 10, Issue 2, October 2022 - March 2023 Page No: 1-13 Research Publish Journals Website: www.researchpublish.com Published Date: 07-October-2022 DOI: https://doi.org/10.5281/zenodo.7157247 Paper Download Link (Source) https://www.researchpublish.com/papers/three-related-problems-of-bergman-spaces-of-tube-domains-over-symmetric-cones
International Journal of Mathematics and Physical Sciences Research, ISSN 2348-5736 (Online), Research Publish Journals, Website: www.researchpublish.com
{"references":["[1]\tD . BEKOLLE - A . BONAMI , Estimates for the Bergman and Szego projections in two symmetric domains . Colloq . Math , 68 , 1995 , 81-100 .","[2]\tD . BEKOLLE - A . BONAMI , Analysis on tube domains over light cones : some extensions of recent results . ActesdesRencontres d' Analyse Complexe : Mars 1999 , Univ . Poitiers Ed . Atlantique et ESA CNRS 6086 , 2000 .","[3]\tD . BEKOLLE - A . BONAMI , - G . GARRIGO'S , Littlewood – Paley decompositions related to symmetric cones . IMHOTEP , to appear ; available at http : //www . harmonic analysis . org .","[4]\tD. BEKOLLE - A . BONAMI , - G . GARRIGO'S - F . RICCI , Littlewood – Paley decompositions and Basov spacesrelated to symmetric cones . Univ . Orleans preprint 2001 ; ; available at http : //www . harmonic analysis . org.","[5]\tD. . BEKOLLE - A . BONAMI – M. PELOSO –F .RICCI ,Boundedness of weighted Bergman projections on tube domains over light cones . Math . Z., 237 , 2001 , 31-59 .","[6]\tD. BEKOLLE - A . TEMGOUA KAGOU, Reproducing properties and L^p- estimates for Bergman projections in Siegel domains of type II . Studia Math ., 115 (3) , 1995 , 219-239 .","[7]\tR. COIFMAN - R. ROCHBERG , Representation theorems for holomorphic functions and harmonic functions in L^p. Asterisque , 77, 1980 , 11-66 .","[8]\tJ. FARAUT –A . KORANYI , Analysis on symmetric cones . Clarendon Press , Oxford 1994","[9]\tC.EFFERMAN , The multiplier problem for the ball . Ann . of Math ., 94 , 1971 , 330 -336 .","[10]\tG. GARRIGO'S, Generalized Hardy spaces on tube domains over cones . Colloq . Math ., 90 ,2001 , 213-251 .","[11]\tE. STEIN , Some problems in harmonic analysis suggested by symmetric spaces and semi- simple Lie groups . Actes , Congres intern , math., 1 , 1970 , 173-189."]}
Databáze: OpenAIRE
Externí odkaz: