论文标题
圆盘和平面小集的亚谐波功能差的积分
Integrals of the difference of subharmonic functions over discs and planar small sets
论文作者
论文摘要
Meromorthic函数的最大模量不能受到此Meromormorphic函数的Nevanlinna特征的限制。但是，来自Meromorthic函数模块对数的积分允许从上方产生类似的限制。 A.A.在古典专着中，Rolf Nevanlinna的重要定理之一说明了这一点。戈德堡和i.v. Ostrovskii在小弧上以及A.F. Grishin，M.L。的小弧及其在文章中的小时间隔的Edrei-Fuchs引理及其版本上的Ostrovskii，以及其版本。 Sodin，T.I。 Malyutina。 B.N.最近获得了亚谐波功能差异积分的相似结果。 Khabiblullin，L.A。Gabdrakhmanova。所有这些结果都取决于射线上亚集的积分。在本文中，我们为圆盘和平面小集合对对数的对数的积分建立了这样的结果。我们的估计值是统一的，因为这些估计值中的常数是明确书写的，并且不依赖于meromormormormormormormormormormormormormormormormormor的函数，并且下谐波函数的差异只要这些函数在零接近零附近具有积分归一化。
The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar restrictions from above. This is illustrated by one of the important theorems of Rolf Nevanlinna in the classical monograph by A.A. Goldberg and I.V. Ostrovskii on meromorphic functions, as well as by the Edrei-Fuchs Lemma on small arcs and its versions for small intervals in articles by A.F. Grishin, M.L. Sodin, T.I. Malyutina. Similar results for integrals of differences of subharmonic functions even with weights were recently obtained by B.N. Khabiblullin, L.A. Gabdrakhmanova. All these results are on integrals over subsets on a ray. In this article, we establish such results for integrals of the logarithm of the modulus of a meromorphic function and the difference of subharmonic functions over discs and planar small sets. Our estimates are uniform in the sense that the constants in these estimates are explicitly written out and do not depend on meromorphic functions and the difference of subharmonic functions provided that these functions has an integral normalization near zero.
