Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

[摘要] 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.

[关键词] Jacobi expansion;potential space;Sobolev space;fractional square function