论文标题
Bloch空间上截短区域功能的估计值
Estimates for truncated area functionals on the Bloch space
论文作者
论文摘要
最近，kayumov \ cite {k}获得了$ n $ th的截断区域的尖锐估算值，用于$ n \ le 5 $在Bloch空间中的归一化功能，然后与Wirths \ cite \ cite {kw1}一起扩展了结果，以$ n = 6 $。我们证明，对于具有非负泰勒系数的功能，相同的急剧估计对于所有$ n $都是有效的。对于任意功能，我们获得了一个渐近的估计值，该估计值在相同的顺序上，但稍大一些（大约为$ 4/e $）。我们还考虑了涉及权力$ n^t $，$ t> 0 $的功能的相关加权估计，并表明指数$ t = 1 $代表了预期尖锐估算的关键案例。
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.
