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Korenblum maximum principle in mixed norm spaces. (English) Zbl 1492.30109

Summary: It is well known that the Korenblum maximum principle holds in Bergman spaces \(\mathrm{A}^p\) if and only if \(p\ge 1\). In this note, we improve this result by proving that the Korenblum maximum principle holds in mixed norm spaces \(\mathrm{H}^{p,q,\alpha}\) when \(1\le p\le q<\infty\) and does not hold when \(0< q< 1\). As an immediate consequence, we obtain that the Korenblum maximum principle holds in weighted Bergman spaces \(\mathrm{A}^p_\gamma\) if and only if \(p\ge 1\).

MSC:

30H20 Bergman spaces and Fock spaces
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