## 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 inequalities
โ Scribed by K. O. Friedrichs
- Publisher
- John Wiley and Sons
- Year
- 1970
- Tongue
- English
- Weight
- 189 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract The best constant in a generalized complex Clarkson inequality is __C__~__p,q__~ (โ) = max {2^1โ1/__p__^ , 2^1/__q__^ , 2^1/__q__ โ1/__p__ +1/2^} which differs moderately from the best constant in the real case __C__~__p,q__~ (โ) = max {2^1โ1/__p__^ , 2^1/__q__^ ,__B__~__p,q__~ }, where
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
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
## 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
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.