Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

Bartosz Langowski

Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)

Résumé

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.

Détail

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

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