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On clarkson's inequalities

โœ Scribed by K. O. Friedrichs


Publisher
John Wiley and Sons
Year
1970
Tongue
English
Weight
189 KB
Volume
23
Category
Article
ISSN
0010-3640

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๐Ÿ“œ SIMILAR VOLUMES


On CLARKSON's Inequalities and Interpola
โœ Lech Maligranda; Lars Erik Persson ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 468 KB

## Abstract We consider some elementary proofs of local versions of CLARKSON's inequalities and point out the fact that these inequalities can be generalized to hold for a much wider class of parameters. In particular it is easy to generalize our interpolation proof in various ways to higher dimens

On Clarkson's inequality in the real cas
โœ Lech Maligranda; Natalia Sabourova ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 206 KB

## Abstract The best constant in a generalized complex Clarkson inequality is __C__~__p,q__~ (โ„‚) = max {2^1โ€“1/__p__^ , 2^1/__q__^ , 2^1/__q__ โ€“1/__p__ +1/2^} which differs moderately from the best constant in the real case __C__~__p,q__~ (โ„) = max {2^1โ€“1/__p__^ , 2^1/__q__^ ,__B__~__p,q__~ }, where

Clarkson and Random Clarkson Inequalitie
โœ Yasuji Takahashi; Mikio Kato ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 367 KB

We first show how ( p , p ' ) Clarkson inequality for a Banach space X is inherited by Lebesgue -Bochner spaces L, (X), which extends C LARKSON'S procedure deriving his inequalities for L, from their scalar versions. Fairly many previous and new results on Clarkson's inequalities, and also those on

Random Clarkson inequalities and LP vers
โœ Andrew Tonge ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 426 KB

In a recent paper KATO [3] uscd the LITTLEWOOD matrices to generalise CLARK-SON'S inequalities. Our first aim is to indicate how KATO'S result can be deduced from a neglected version of the HAUSDORFP-YOUXG inequnlity which was proved by WELLS m c t WILLIAXS [12]. \Ve next establish "random CLARKSON

Type, Cotype Constants and Clarkson's In
โœ Mikio Kato; Yasuji Takahashi ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 389 KB

## It is shown that a Banach space satisfies Clarkson's inequalities if and only if its "type or cotype constant" is 1, which implies in particular that the notions of Goand G, -Fourier type by I " (161 are equivalent. A sequence of related results is also given. 1991 Maihemaiics Subject Clarrifi

Generalized Clarkson's Inequalities and
โœ Mikio Kato ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 245 KB

By using the LITTLEWOOD matrices B g n we generalize CLAEKSON'S inequelitiee, or equivalently, we determine the norms IIAzn : Z,2"(Lp) + Zr(Lp)ll completely. The result is compared with the norms IIAp : 1,2" -+ Zrl l , which are calculated implicitly in PIETSOE [el.