We itre concerned with existence of extensions of positive linear operators be-I t v w i i ordered vector spaces which take maximal possible values on a given set of \wit ors. We eatablish a criterion (Theorem) which partially generalizes a similar twiilt of [2] about positive additive set functions
Vector-Valued Extensions of Operators on Martingales
โ Scribed by Sergio Antonio Tozoni
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 262 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
โฆ Synopsis
We study weighted inequalities for vector valued extensions of the conditioned square function operator and of the maximal operators of matrix type in the case of regular martingales. As applications we obtain weighted inequalities for vectorvalued extensions of the HardyแLittlewood maximal operator and of singular integral transforms on martingales.
๐ SIMILAR VOLUMES
## Abstract In this paper we consider extensions of bounded vectorโvalued holomorphic (or harmonic or pluriharmonic) functions defined on subsets of an open set ฮฉ โ โ^__N__^ . The results are based on the description of vectorโvalued functions as operators. As an application we prove a vectorโvalue
## Abstract It is shown that a Banach space __E__ has type __p__ if and only for some (all) __d__ โฅ 1 the Besov space __B__^(1/__p__ โ 1/2)__d__^ ~__p__,__p__~ (โ^__d__^ ; __E__) embeds into the space __ฮณ__ (__L__^2^(โ^__d__^ ), __E__) of __ฮณ__ โradonifying operators __L__^2^(โ^__d__^ ) โ __E__. A