On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Maligranda, Lech¹  Mykhaylyuk, Volodymyr V.²  Plichko, Anatolij³ 

[1] Lulea Univ Technol, Dept Math, SE-97187 Lulea, Sweden

[2] Chernivtsi Natl Univ, Dept Appl Math, UA-58012 Chernovtsy, Ukraine

[3] Cracow Univ Technol, Inst Math, PL-31155 Krakow, Poland

关键词: Absolutely continuous functions;    Lipschitz functions;    Superpositions;    Absolutely continuous functions of two variables;    Embeddings;    Strictly singular embeddings;    Superstrictly singular embeddings;    Beppo Levi spaces;    Sobolev spaces;    Rearrangement invariant spaces;   

DOI  :  10.1016/j.jmaa.2010.09.027

来源: Elsevier

【 摘 要 】

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the embeddings of Banach spaces point of view. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free