Generalized Dunkl-Lipschitz Spaces

Abstract

This paper deals with generalized Lipschitz spaces ${\wedge }_{\alpha ,p,q}^k(\mathbb{R})$ in the context of Dunkl harmonic analysis on $\mathbb{R}$, for all real $\alpha$. It also introduces a generalized Dunkl-Lipschitz spaces $\mathcal{T}{\wedge }_{\alpha ,p,q}^k({\mathbb{R}}_{+}^2)$ of $k$-temperature on ${\mathbb{R}}_{+}^2$. Some properties and continuous embedding of these spaces and the isomorphism of $\mathcal{T}{\wedge }_{\alpha ,p,q}^k({\mathbb{R}}_{+}^2)$ and ${\wedge }_{\alpha ,p,q}^k(\mathbb{R})$ are established.

References in corpus (1)

• Various characterizations of Besov-Dunkl spaces