Weighted composition operators on weighted Bergman spaces induced by doubling weights - Du, Juntao; Li, Songxiao; Shi, Yecheng (MATHEMATICA SCANDINAVICA, 2020)
In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_φ $ on Bergman type spaces $A_ω ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_φ \colon A_ω ^p→ A_ω ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^∞ $ if and only if ϕ is a finite Blaschke product.