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arXiv · 2307.14699

Korenblum's principle for Bergman spaces with radial weights

Iason Efraimidis·Adrián Llinares·Dragan Vukotić
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Abstract

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces $A^p_w$ with arbitrary (non-negative and integrable) radial weights $w$ in the case $1\le p<\infty$. We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption $\liminf_{r\to 0^+} w(r)>0$, we show that the principle fails whenever $0<p<1$.

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Iason Efraimidis, Adrián Llinares, Dragan Vukotić. 2023-07-27. Korenblum's principle for Bergman spaces with radial weights. https://doi.org/10.1007/s40315-024-00543-6

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