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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147141 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531545498124288 |
|---|---|
| author | Langowski, B. |
| author_facet | Langowski, B. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-24T04:38:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147141 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:38:49Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Langowski, B. 2019-02-13T17:25:21Z 2019-02-13T17:25:21Z 2015 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 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions Article published earlier |
| spellingShingle | Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions Langowski, B. |
| title | 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_short | Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions |
| title_sort | potential and sobolev spaces related to symmetrized jacobi expansions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147141 |
| work_keys_str_mv | AT langowskib potentialandsobolevspacesrelatedtosymmetrizedjacobiexpansions |