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The authors consider weighted Bergman spaces of holomorphic $L\sp p\/$ integrable functions with respect to certain Borel measures on a bounded plane region. A closed subspace $\scr M $ of such a space is said to be invariant if $z {\scr M} \subset {\scr M}$. In the case of the standard Bergman space of the unit disk with $p = 2$, the authors proved in a recent joint paper with C. Sundberg [Acta M
