Vector Fourier analysis on compact groups and Assiamoua spaces

This paper shows how a family of function spaces (coined as Assiamoua spaces) plays a fundamental role in the Fourier analysis of vector-valued functions compact groups. These spaces make it possible to transcribe the classic results of Fourier analysis in the framework of analysis of vector-valued functions and vector measures. The construction of Sobolev spaces of vector-valued functions on compact groups rests heavily on the members of the aforementioned family.