Sobolev spaces of vector-valued functions on  compact groups

Yaogan Mensah

Vol. 30 No. 1 (2025)

Regular Articles

Sobolev spaces of vector-valued functions on compact groups

Published 2025-03-11

Yaogan Mensah

Yaogan Mensah
University of Lomé

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

Abstract

This paper deals with a class of Sobolev spaces of vector-valued functions on a compact group. Using some results among which are the inversion formula and the Plancherel type theorem involving the Fourier transform of vector-valued functions, we define Sobolev spaces of Bessel potential type. Then, some Sobolev embedding theorems are proved.

Keywords

vector-valued function, Fourier transform, Sobolev space, Sobolev embedding theorem

PDF

Supplementary File(s)

5253-15459-1-SP - final

Author Biography

Yaogan Mensah

Department of Mathematics