Composition operators on analytic Lipschitz spaces

If $X$ is a Banach space of functions analytic on the disk and $\varphi :{\mathbf{D}} \to {\mathbf{D}}$ is analytic, one can define the composition operator ${C_\varphi }$ on $X$ by ${C_\varphi }f: = f \circ \varphi$. This paper discusses the boundedness and $w$-compactness of composition operators on the analytic Lipschitz spaces ${\mathcal{A}_\alpha },\;0 < \alpha < 1$.