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Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions
Інший ID:
2010 Mathematics Subject Classification: 42C10; 42C05; 42C20
DOI:10.3842/SIGMA.2015.073
DOI:10.3842/SIGMA.2015.073
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
458
Завантажень:
229
Анотація:
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.
