Dunkl heat semigroup and applications

Abstract

In this article we characterize the Dunkl–Besov spaces and prove the embedding Sobolev theorems via the Dunkl heat semigroup. We also study the dispersive properties of the solutions of the Dunkl heat equation. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems on generalized functional spaces.

Keywords:

• Dunkl heat semigroups
• Strichartz estimates
• nonlinear Dunkl heat equation
• local and global well-posedness

AMS Subject Classifications::

• Primary: 35L05
• Secondary: 22E30

Acknowledgements

The author gratefully acknowledges the Deanship of Scientic Research at the University of King Faisal on material and moral support in the financing of this research project No. 130172. The author is deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article.