Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions
We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among further results, we obtain a fractional square function charact...
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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions / B. Langowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 29 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-147141 |
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oai:nasplib.isofts.kiev.ua:123456789-1471412025-02-23T17:39:51Z Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions Langowski, B. We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among further results, we obtain a fractional square function characterization, structural theorems and Sobolev type embedding theorems for these potential spaces. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications. The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html. The author would like to express his gratitude to Professor Adam Nowak for indicating the topic and constant support during the preparation of this paper. Research supported by the National Science Centre of Poland, project No. 2013/09/N/ST1/04120. 2015 Article Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions / B. Langowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 29 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C10; 42C05; 42C20 DOI:10.3842/SIGMA.2015.073 https://nasplib.isofts.kiev.ua/handle/123456789/147141 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among further results, we obtain a fractional square function characterization, structural theorems and Sobolev type embedding theorems for these potential spaces. |
| format |
Article |
| author |
Langowski, B. |
| spellingShingle |
Langowski, B. Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Langowski, B. |
| author_sort |
Langowski, B. |
| title |
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions |
| title_short |
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions |
| title_full |
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions |
| title_fullStr |
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions |
| title_full_unstemmed |
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions |
| title_sort |
potential and sobolev spaces related to symmetrized jacobi expansions |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| citation_txt |
Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions / B. Langowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 29 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-22T04:24:17Z |
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2025-07-22T04:24:17Z |
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