Normal Families of Discrete Open Mappings with Controlled p-Module

被引：16

作者：

Golberg, Anatoly ^{[1
]}

Salimov, Ruslan ^{[2
]}

Sevost'yanov, Evgeny ^{[3
]}

机构：

[1] Holon Inst Technol, Dept Appl Math, 52 Golomb St,POB 305, IL-5810201 Holon, Israel

[2] Natl Acad Sci Ukraine, Inst Math, 3 Tereschenkivska St, UA-01601 Kiev 4, Ukraine

[3] Zhitomir Ivan Franko State Univ, Dept Math Anal, 40 Bolshaya Berdichevskaya St, UA-10008 Zhitomir, Ukraine

来源：

COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS VI, PT 2: COMPLEX ANALYSIS, QUASICONFORMAL MAPPINGS, COMPLEX DYNAMICS | 2016年 / 667卷

关键词：

Weighted p-module; ring Q-mappings; Lipschitz mappings; quasi-conformality in the mean; equicontinuity; normal families;

D O I：

10.1090/conm/667/13533

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the generic discrete open mappings in R-n under which the perturbation of extremal lengths of curve collections is controlled integrally via integral Q(x)eta(p)(vertical bar x - x(0)vertical bar)dm(x) with n - 1 < p < n, where Q is a measurable function on R-n and integral(r2)(r1) eta(r)dr >= 1 for any eta on a given interval [r(1), r(2)]. We prove that the family of all open discrete mappings of above type is normal under appropriate restrictions on the majorant Q.

引用

页码：83 / 103

页数：21

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