A Subspace of Hölder Space Consisting Only of Nonsmoothest Functions

被引：0
作者：
E. I. Berezhnoi
机构：
[1] P. G. Demidov Yaroslavl State University,
来源：
Mathematical Notes | 2003年 / 74卷
关键词：
Hölder space; Banach space; nonsmooth function; modulus of continuity; set of first category;
D O I：
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学科分类号：
摘要：
In the first part of this paper, we give a complete answer to an old question of the geometric theory of Banach spaces; namely, we construct an infinite-dimensional closed subspace of Hölder space such that each function not identically zero is not smoother at each point than the nonsmoothest function in Hölder space. In the second part, using constructions from the first part, we show that the set of functions from Hölder space which are smoother on a set of positive measure than the nonsmoothest function is a set of first category in this space.
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页码：316 / 325
页数：9
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