Abstract Suppose that $\alpha>1$. Let $u$ be analytic in the unit disc $D$ and $\varphi$ be analytic map-self on $D$. In the paper, the authors give the simple necessary and sufficient condition of the weighted composition operator $uC_{\varphi}$ being compact from $\beta_{L}$ to $\beta_{\alpha}$ on $D$.
GUAN Ying, LI Min, ZHANG Xue-jun. A kind of improvement about compactness condition of composition type operator between Logarithm weight Bloch space in the disc. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 205-210.
