|
Session 18. Harmonic analysis, orthogonal expansions and Dunkl theory
|
On Sobolev and potential spaces related to Jacobi expansions |
Bartosz Langowski, Wroclaw University of Technology, Poland
|
|
|
We define and study Sobolev spaces associated with Jacobi expansions. We prove that
these Sobolev spaces are isomorphic, in the Banach space sense, with potential spaces (for the Jacobi `Laplacian')
of the same order. This is an essential generalization and strengthening of the recent results [1] concerning the special case of ultraspherical
expansions, where in addition a restriction on the parameter of type was imposed. We also present some further results and applications, including a variant of Sobolev embedding theorem.
Moreover, we give a characterization of the Jacobi potential spaces of arbitrary order in terms of suitable fractional square functions. As an auxiliary result of independent interest we prove \(L^p\)-boundedness of these fractional square functions.
|
|
|
References-
J.J. Betancor, J.C. Fariña, L. Rodriguez-Mesa, R. Testoni, J.L. Torrea, A
choice of Sobolev spaces associated with ultraspherical expansions, Publ. Math.
54 (2010), 221-242.
-
B. Langowski,
Sobolev spaces associated with Jacobi expansions , preprint (2013). arXiv:1312.7285
-
B. Langowski,
On potential spaces related to Jacobi expansions , preprint (2014).
|
|
| Print version |
|
