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On Clarkson's inequality in the real case

✍ Scribed by Lech Maligranda; Natalia Sabourova

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 206 KB
Volume: 280
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200610552

No coin nor oath required. For personal study only.

✦ Synopsis

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)

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