In this paper we define difference operators and homogeneous Sobolev-type spaces on the dual of a compact Lie group. As an application and to show that this defines a relevant differential structure, we state and prove multiplier theorems of Hörmander, Mihlin and Marcinkiewicz types together with the sharpness in the Sobolev exponent for the result of Hörmander type.
- Differential calculus over a non-commutative algebra
- Harmonic analysis on compact Lie groups
- Homogeneous Sobolev spaces
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