Difference of composition operators between weighted Bergman spaces on the unit ball

Abstract

We obtain some estimates for norm and essential norm of the difference of two composition operators between weighted Bergman spaces $A_{\alpha }^p$ and $A_{\beta }^q$ on the unit ball. In particular, we completely characterize the boundedness and compactness of $C_{\phi }-C_{\psi }:A_{\alpha }^p\to A_{\beta }^q$ for full range $0<p,q<\infty$, $-1<\alpha ,\beta <\infty$.

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