Sobolev spaces of vector-valued functions on compact groups

Yaogan Mensah

doi:10.64785/mc.30.1.9

March 11, 2025Mathematical communicationsOpen Access

Sobolev spaces of vector-valued functions on compact groups

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Key Points

Sobolev spaces of vector-valued functions are defined using the fourier transform and its related theorems.
Key results include the establishment of continuous embedding theorems within these sobolev spaces.
The study applies inversion formulas and the plancherel theorem to enhance understanding of these spaces.
These findings contribute to the theory of functional spaces on compact groups, indicating potential applications.

Implication

This paper defines sobolev spaces for vector-valued functions on compact groups, highlighting continuity results.

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 continuous embedding results are proved.

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Cite This Study

Yaogan Mensah (2025) studied this question.

synapsesocial.com/papers/68c18c019b7b07f3a06144b9 https://doi.org/10.64785/mc.30.1.9

View Full Paper

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Sobolev spaces of vector-valued functions on compact groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Sobolev spaces of vector-valued functions on compact groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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