This article is cited in 3 papers

Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

Bartosz Langowski

Wydział Matematyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50–370 Wrocław, Poland

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.

Keywords: Jacobi expansion; potential space; Sobolev space; fractional square function.

MSC: 42C10; 42C05; 42C20

Received: May 8, 2015; in final form September 10, 2015; Published online September 12, 2015

Language: English

DOI: 10.3842/SIGMA.2015.073

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ArXiv: 1505.01653