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Sobolev spaces on compact groups

  • Manoj Kumar and N. Shravan Kumar ORCID logo EMAIL logo
Published/Copyright: April 27, 2023

Abstract

In this note, we introduce Sobolev spaces over (not necessarily abelian) compact groups and study their properties. In particular, we focus on Sobolev embedding and compactness theorems. As an application, we prove the existence of solutions for the generalized Bosonic equations posed over compact groups.

MSC 2020: 43A30; 43A77; 22C05

Communicated by Jan Frahm


Funding statement: The author Manoj Kumar is supported by the NBHM post-doctoral fellowship with reference number 0204/3/2021/R&D-II/7356.

Acknowledgements

The authors would like to thank the referee for his perspicuous comments and suggestions which helped in improving the quality of the paper.

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Received: 2022-03-07
Revised: 2023-01-21
Published Online: 2023-04-27
Published in Print: 2023-07-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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