Sobolev spaces of vector-valued functions on compact groups

TL;DR

This paper explores Sobolev spaces of vector-valued functions on compact groups, establishing embedding theorems that extend classical results to this setting.

Contribution

It introduces Sobolev spaces for vector-valued functions on compact groups and proves new embedding theorems for these spaces.

Findings

Proved Sobolev embedding theorems for vector-valued functions on compact groups.

Extended classical Sobolev space results to the setting of compact groups.

Provided foundational results for analysis on vector-valued function spaces on groups.

Abstract

This paper deals with a class of Sobolev spaces of vector-valued functions on a compact group. Some Sobolev embedding theorems are proved.