Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 073, 17 pages      arXiv:1505.01653      https://doi.org/10.3842/SIGMA.2015.073
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications

Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

Bartosz Langowski
Wydział Matematyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

Received May 08, 2015, in final form September 10, 2015; Published online September 12, 2015

Abstract
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.

Key words: Jacobi expansion; potential space; Sobolev space; fractional square function.

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