Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones
Abstract: 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, rel...
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ftzenodo:oai:zenodo.org:7157247 2023-06-06T11:58:59+02:00 Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones Sami Ali Obaid.B. A. A Ahmed Sufyan Abakar Shawgy Hussein 2022-10-07 https://zenodo.org/record/7157247 https://doi.org/10.5281/zenodo.7157247 eng eng issn:2348-5736 https://www.researchpublish.com/papers/three-related-problems-of-bergman-spaces-of-tube-domains-over-symmetric-cones doi:10.5281/zenodo.7157246 https://zenodo.org/record/7157247 https://doi.org/10.5281/zenodo.7157247 oai:zenodo.org:7157247 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/4.0/legalcode International Journal of Mathematics and Physical Sciences Research 10(2) 1-13 Whitney decomposition Symmetric cone Bergman projector Littlewood – Paley Hardy inequality Paper Download Link (Source) info:eu-repo/semantics/article publication-article 2022 ftzenodo https://doi.org/10.5281/zenodo.715724710.5281/zenodo.7157246 2023-04-13T21:56:03Z Abstract: 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 Article in Journal/Newspaper sami Zenodo |
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English |
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Whitney decomposition Symmetric cone Bergman projector Littlewood – Paley Hardy inequality Paper Download Link (Source) |
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Whitney decomposition Symmetric cone Bergman projector Littlewood – Paley Hardy inequality Paper Download Link (Source) Sami Ali Obaid.B. A. A Ahmed Sufyan Abakar Shawgy Hussein Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones |
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Whitney decomposition Symmetric cone Bergman projector Littlewood – Paley Hardy inequality Paper Download Link (Source) |
description |
Abstract: 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 |
format |
Article in Journal/Newspaper |
author |
Sami Ali Obaid.B. A. A Ahmed Sufyan Abakar Shawgy Hussein |
author_facet |
Sami Ali Obaid.B. A. A Ahmed Sufyan Abakar Shawgy Hussein |
author_sort |
Sami Ali |
title |
Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones |
title_short |
Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones |
title_full |
Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones |
title_fullStr |
Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones |
title_full_unstemmed |
Three Related Problems of Bergman Spaces of Tube Domains over Symmetric Cones |
title_sort |
three related problems of bergman spaces of tube domains over symmetric cones |
publishDate |
2022 |
url |
https://zenodo.org/record/7157247 https://doi.org/10.5281/zenodo.7157247 |
genre |
sami |
genre_facet |
sami |
op_source |
International Journal of Mathematics and Physical Sciences Research 10(2) 1-13 |
op_relation |
issn:2348-5736 https://www.researchpublish.com/papers/three-related-problems-of-bergman-spaces-of-tube-domains-over-symmetric-cones doi:10.5281/zenodo.7157246 https://zenodo.org/record/7157247 https://doi.org/10.5281/zenodo.7157247 oai:zenodo.org:7157247 |
op_rights |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/4.0/legalcode |
op_doi |
https://doi.org/10.5281/zenodo.715724710.5281/zenodo.7157246 |
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1767948296074035200 |