On Bounded Second Variation

• 作者: J. L. Sánchez José Giménez Lorena López N. Merentes
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: FUNCTION of BOUNDED VARIATION LIPSCHITZ CONTINUOUS FUNCTION Absolutely CONTINUOUS FUNCTION Nemytskij OPERATOR
• 年，卷（期）: 2012,（1）
• 页码范围: 22-26
• 页数: 5页
• 分类号: O1

摘要

In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator Sg maps BV''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV''loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1), A2p