We define and study the Bessel potential and inhomogeneous Besov spaces associated with the Dunkl operators on Rd. As applications on these spaces we construct the Sobolev type embedding theorem and the paraproduct operators associated with the Dunkl operators, as similar to those defined by Bony. We also establish Strichartz type estimates for the Dunkl-Schrödinger equation and finally we study the problem of well posedness of the generalized heat equation.
- Differential-difference equations
- Dunkl operators
- Inhomogeneous dunkl-besov space
- Inhomogeneous dunkl-triebel-lizorkin space
- Littlewood-Paley decomposition
- Paraproduct operator
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