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On Clarkson's inequality in the real case
Author(s) -
Maligranda Lech,
Sabourova Natalia
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610552
Subject(s) - mathematics , lp space , constant (computer programming) , norm (philosophy) , inequality , combinatorics , pure mathematics , mathematical analysis , banach space , computer science , law , political science , programming language
Abstract The best constant in a generalized complex Clarkson inequality is C p,q (ℂ) = max {2 1–1/ p , 2 1/ q , 2 1/ q –1/ p +1/2 } which differs moderately from the best constant in the real case C p,q (ℝ) = max {2 1–1/ p , 2 1/ q , B p,q }, where . For 1 < q < 2 < p < ∞ the constant C p,q (ℝ) is equal to B p,q and these numbers are difficult to calculate in general. As applications of the generalized Clarkson inequalities the ( p, q )‐Clarkson inequalities in Lebesgue spaces, in mixed norm spaces and in normed spaces are presented. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)