标题： 自改进的次调和函数和解析函数增长估计 显示英文标题

标题： Self-improving estimates of growth of subharmonic and analytic functions

摘要： 给定一个有界开子集$\Omega$和闭子集$A,B$of$\mathbb{R}^k$，我们讨论当一个估计$u(x)\le g(dist(x,A\cup B))$，$x\in\Omega\setminus(A\cup B)$对于在$\Omega\setminus B$上次调和的函数$u$时，意味着$u(x)\le h(dist(x,B))$，$x\in\Omega\setminus B$，其中$g,h:(0,\infty)\to (0,\infty)$是递减函数且$g(0^+)=h(0^+)=\infty$。 我们寻求$h$的显式表达式，以$g$表示。 我们给出了一些此类结果，并表明 Domar 的工作（On the existence of a largest subharmonic minorant of a given function, Ark. Mat., 3 (1957), pp. 429-440）允许由此推导出此方向的其他结果。 然后我们比较这两种方法。 对于解析函数的估计也得到了类似的结果。 显示英文摘要

摘要： Given a bounded open subset $\Omega$ and closed subsets $A,B$ of $\mathbb{R}^k$, we discuss when an estimate $u(x)\le g(dist(x,A\cup B))$, $x\in\Omega\setminus(A\cup B)$, for a function $u$ subharmonic on $\Omega\setminus B$, implies that $u(x)\le h(dist(x,B))$, $x\in\Omega\setminus B$, where $g,h:(0,\infty)\to (0,\infty)$ are decreasing functions and $g(0^+)=h(0^+)=\infty$. We seek for explicit expressions of $h$ in terms of $g$. We give some results of this type and show that Domar's work (On the existence of a largest subharmonic minorant of a given function, Ark. Mat., 3 (1957), pp. 429-440) permits one to deduce other results in this direction. Then we compare these two approaches. Similar results are deduced for estimates of analytic functions.