Sharp L p Bound for Holomorphic Functions on the Unit Disc

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• 作者：Adam Osȩkowski
• 关键词：Primary 31B05 ; Secondary 30J99 ; Harmonic function ; holomorphic function ; best constants
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：13
• 期：1
• 页码：127-139
• 全文大小：541 KB
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• 作者单位：Adam Osȩkowski (1)
  
  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

For any 1 < p < ∞ and any \({X, Y\in \mathbb{R}}\) satisfying \({|X|\leq Y}\) , we determine the optimal constant C _p (X,Y) such that the following holds. If F is a holomorphic function on the unit disc satisfying ReF(0) = X and \({||{\rm Re}F||_{L^{p}(\mathbb{T})}=Y}\) , then $$||F||_{L^p(\mathbb{T})}\geq C_p(X,Y).$$