On submultiplicativity of an N-function and its conjugate

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• 作者：Lech Maligranda
• 关键词：46E30 ; 46B20 ; 46B42 ; Orlicz functions ; submultiplicative functions ; power function
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：89
• 期：3
• 页码：569-573
• 全文大小：408 KB
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• 作者单位：Lech Maligranda (1)
  
  1. Department of Engineering Sciences and Mathematics, Lule? University of Technology, 971 87, Lule?, Sweden
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Combinatorics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8903

文摘

It is shown that if an N-function φ is submultiplicative, then its conjugate function φ* cannot be submultiplicative. Moreover, we have the following characterization of power functions among N-functions: if an N-function φ is C ₁-submultiplicative and its conjugate function φ* is C ₂-submultiplicative for some C ₁, C ₂ >? 0, then φ is equivalent to a power function.