Abstract
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 \(p\ge 1\).
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The author is supported in part by the Serbian Ministry of Education, Science and Technological Development, Project #174032.
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Karapetrović, B. Korenblum maximum principle in mixed norm spaces. Arch. Math. 118, 497–507 (2022). https://doi.org/10.1007/s00013-022-01723-3
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DOI: https://doi.org/10.1007/s00013-022-01723-3