On the deformed Besov-Hankel spaces
In this paper we introduce function spaces denoted by \(BH_{\kappa,\beta}^{p,r}\) (\(0\lt\beta\lt 1\), \(1\leq p, r \leq +\infty\)) as subspaces of \(L^p\) that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case \(1\leq p\le...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2020-03-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol40/2/art/opuscula_math_4010.pdf |
| _version_ | 1818616141899104256 |
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| author | Salem Ben Saïd Mohamed Amine Boubatra Mohamed Sifi |
| author_facet | Salem Ben Saïd Mohamed Amine Boubatra Mohamed Sifi |
| author_sort | Salem Ben Saïd |
| collection | DOAJ |
| description | In this paper we introduce function spaces denoted by \(BH_{\kappa,\beta}^{p,r}\) (\(0\lt\beta\lt 1\), \(1\leq p, r \leq +\infty\)) as subspaces of \(L^p\) that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case \(1\leq p\leq +\infty\) and in terms of partial Hankel integrals in the case \(1\lt p\lt +\infty\) associated to the deformed Hankel operator by a parameter \(\kappa\gt 0\). For \(p=r=+\infty\), we obtain an approximation result involving partial Hankel integrals. |
| first_indexed | 2024-12-16T16:45:05Z |
| format | Article |
| id | doaj.art-49f42c9cda974c998286777f5f6cd799 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-16T16:45:05Z |
| publishDate | 2020-03-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-49f42c9cda974c998286777f5f6cd7992022-12-21T22:24:12ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742020-03-01402171207https://doi.org/10.7494/OpMath.2020.40.2.1714010On the deformed Besov-Hankel spacesSalem Ben Saïd0https://orcid.org/0000-0001-7577-5167Mohamed Amine Boubatra1https://orcid.org/0000-0002-3595-7246Mohamed Sifi2https://orcid.org/0000-0003-0607-8303Department of Mathematical Science, College of Science, United Arab Emirates University, Al-Ain, Abu Dhabi, UAEUniversité Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d'Analyse Mathématique et Applications, LR11ES11, Campus Universitaire, 2092 El Manar I, Tunis, TunisiaUniversité Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire d'Analyse Mathématique et Applications, LR11ES11, Campus Universitaire, 2092 El Manar I, Tunis, TunisiaIn this paper we introduce function spaces denoted by \(BH_{\kappa,\beta}^{p,r}\) (\(0\lt\beta\lt 1\), \(1\leq p, r \leq +\infty\)) as subspaces of \(L^p\) that we call deformed Besov-Hankel spaces. We provide characterizations of these spaces in terms of Bochner-Riesz means in the case \(1\leq p\leq +\infty\) and in terms of partial Hankel integrals in the case \(1\lt p\lt +\infty\) associated to the deformed Hankel operator by a parameter \(\kappa\gt 0\). For \(p=r=+\infty\), we obtain an approximation result involving partial Hankel integrals.https://www.opuscula.agh.edu.pl/vol40/2/art/opuscula_math_4010.pdfdeformed hankel kernelbesov spacesbochner-riesz meanspartial hankel integrals |
| spellingShingle | Salem Ben Saïd Mohamed Amine Boubatra Mohamed Sifi On the deformed Besov-Hankel spaces Opuscula Mathematica deformed hankel kernel besov spaces bochner-riesz means partial hankel integrals |
| title | On the deformed Besov-Hankel spaces |
| title_full | On the deformed Besov-Hankel spaces |
| title_fullStr | On the deformed Besov-Hankel spaces |
| title_full_unstemmed | On the deformed Besov-Hankel spaces |
| title_short | On the deformed Besov-Hankel spaces |
| title_sort | on the deformed besov hankel spaces |
| topic | deformed hankel kernel besov spaces bochner-riesz means partial hankel integrals |
| url | https://www.opuscula.agh.edu.pl/vol40/2/art/opuscula_math_4010.pdf |
| work_keys_str_mv | AT salembensaid onthedeformedbesovhankelspaces AT mohamedamineboubatra onthedeformedbesovhankelspaces AT mohamedsifi onthedeformedbesovhankelspaces |