Sobolev spaces of vector-valued functions on compact groups

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.