In this paper, we give estimates on partial derivatives and logarithmic partial derivatives for holomorphic functions on polydiscs. Estimates will also be utilized to characterize entire solutions of a class of partial differential equations, which gives a new form of Picard’s theorem and its higher dimensional version.

中文翻译：

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多碟上的全纯函数的偏导数和对数偏导数的估计。

在本文中，我们给出了多碟上全纯函数的偏导数和对数偏导数的估计。估计值还将用于表征一类偏微分方程的整体解，从而给出了Picard定理及其更高维版本的新形式。