Uniformly bounded composition operators in the Banach space of absolutely continuous functions

被引：2

作者：

Glazowska, D. ^{[1
]}

Matkowski, J. ^{[1
]}

Merentes, N. ^{[2
]}

Sanchez Hernandez, J. L. ^{[2
]}

机构：

[1] Univ Zielona Gora, Fac Math Comp Sci & Econometr, PL-65516 Zielona Gora, Poland

[2] Cent Univ Venezuela, Dept Matemat, Caracas 1220A, Venezuela

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 13期

关键词：

Composition operator; Nemytskij operator; Bounded operator; Uniformly bounded operator; Equidistantly uniformly bounded operator; Lipschitzian operator; Uniformly continuous operator; Banach space of absolutely continuous functions;

D O I：

10.1016/j.na.2012.04.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let I, J subset of R be intervals and let h : I x J -> R be an arbitrary function. Our main result says that if the Nemytskij composition operator H of the generator h mapping the set AC(I, J) into the Banach space AC(I, R) is uniformly bounded (or equidistantly uniformly bounded), then h(x, y) = a(x)y + b(x), x is an element of I, y is an element of R, for some functions a, b is an element of AC(I, R). (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：4995 / 5001

页数：7

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