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