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Generalized Dunkl-Lipschitz Spaces (1402.7339v1)
Published 26 Feb 2014 in math.FA
Abstract: This paper deals with generalized Lipschitz spaces $\wedgek_{\alpha,p,q}(\R)$ in the context of Dunkl harmonic analysis on $\R$, for all real $\alpha$. It also introduces a generalized Dunkl-Lipschitz spaces ${\cal T}\wedgek_{\alpha,p,q}(\R2_+)$ of $k$-temperature on $\R2_+$. Some properties and continuous embedding of these spaces and the isomorphism of ${\cal T}\wedgek_{\alpha,p,q}(\R2_+)$ and $\wedgek_{\alpha,p,q}(\R)$ are established.