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arXiv · 2208.10626

Estimates for truncated area functionals on the Bloch space

Iason Efraimidis·Alejandro Mas·Dragan Vukotić
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Abstract

Recently, Kayumov \cite{K} obtained a sharp estimate for the $n$-th truncated area functional for normalized functions in the Bloch space for $n\le 5$ and then, together with Wirths \cite{KW1}, extended the result for $n=6$. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all $n$. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of $4/e$). We also consider related weighted estimates for functionals involving the powers $n^t$, $t>0$, and show that the exponent $t=1$ represents the critical case for the expected sharp estimate.

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Iason Efraimidis, Alejandro Mas, Dragan Vukotić. 2022-08-22. Estimates for truncated area functionals on the Bloch space. https://arxiv.org/abs/2208.10626

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