A scalar sequence β£ is said to be a p-summing multiplier of a Banach space i Ο± 5 5 p E, if Γ β£ x -Ο± for all weakly p-summable sequences in E. We study some Ε½ . important properties of the space m E of all p-summing multipliers of E, p consider applications to E-valued operators on the sequence spa
Absolutely Summing Multipliers on Hp Spaces
β Scribed by Ibrahim Almasri
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 95 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
and f is called a little β£-Bloch function, denoted by Ε½ . Ε½ . where g z, a is a Green's function of D D with singularity at a. Similarly, an analytic function f belongs to Q , 0p -Ο±, if p, 0 < < 2 p lim f Π z g z, a dxdy s 0.
## Abstract Using Herz spaces, we obtain a sufficient condition for a bounded measurable function on β^__n__^ to be a Fourier multiplier on __H^p^~Ξ±~__ (β^__n__^ ) for 0 < __p__ < 1 and β__n__ < Ξ± β€ 0. Our result is sharp in a certain sense and generalizes a recent result obtained by Baernstein an
## Abstract Let __X__ be a Banach space. We show that each __m__ : β \ {0} β __L__ (__X__ ) satisfying the Mikhlin condition sup~__x__ β 0~(β__m__ (__x__ )β + β__xm__ β²(__x__ )β) < β defines a Fourier multiplier on __B__ ^__s__^ ~__p,q__~ (β; __X__ ) if and only if 1 < __p__ < β and __X__ is isomorp