Abstract: The Szego projection of tube domains over irreducible symmetric cones is unbounded in L(1+ϵ). 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 1+ϵ 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
