Fractional smoothness in $L^p$ with Dunkl weight and its applications

Abstract

We define fractional power of the Dunkl Laplacian, fractional modulus of smoothness and fractional $K$-functional in $L^p$-space with the Dunkl weight. As application, we prove direct and inverse theorems of approximation theory, and some inequalities for entire functions of spherical exponential type in fractional settings.

28 pages. arXiv admin note: text overlap with arXiv:1703.06830