Abstract
In this paper we obtain a necessary and sufficient condition on the weighted vector-valued function \(\varphi =(\varphi _1, \ldots , \varphi _n)\) for which each function analytic in the unit polydisc that has no zero and belongs in \(A^p(\varphi )\) is weakly invertible in the space \(A^q(\varphi )\) for any \(0<q<p<+\infty \).
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