## Abstract Let __X__(ΞΌ) be a Banach function space. In this paper we introduce two new geometric notions, __q__βconvexity and weak __q__βconvexity associated to a subset __S__ of the unit ball of the dual of __X__(ΞΌ), 1 β€ __q__ < β. We prove that in the general case both notions are not equivalent
On the Davis inequality in Banach function spaces
β Scribed by Masato Kikuchi
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 172 KB
- Volume
- 281
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We give a characterization of those Banach function spaces in which the Davis inequality for martingales is valid. (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
π SIMILAR VOLUMES
The paper is devoted to some results on the problem of S. M. Ulam for the stability of functional equations in Banach spaces. The problem was posed by Ulam 60 years ago.
## Abstract Let __X__ be a real Banach space, __Ο__ : [0, +β) β β be an increasing continuous function such that __Ο__(0) = 0 and __Ο__(__t__ + __s__) β€ __Ο__(__t__) + __Ο__(__s__) for all __t__, __s__ β [0, +β). According to the infinite dimensional analog of the Osgood theorem if β«^1^~0~ (__Ο__(_