Potential and Sobolev Spaces Related to Symmetrized Jacobi Expansions

Symmetry Integrability and Geometry-Methods and Applications

article

Bartosz Langowski¹ 

[1] Wydział Matematyki, Politechnika Wrocławska

关键词: Jacobi expansion;    potential space;    Sobolev space;    fractional square function;   

DOI  :  10.3842/SIGMA.2015.073

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown