We investigate how the entropy numbers (e n (T )) of an arbitrary Ho lder-continuous operator T: E Γ C(K ) are influenced by the entropy numbers (= n (K )) of the underlying compact metric space K and the geometry of E. We derive diverse universal inequalities relating finitely many = n (K )'s with
Entropy Numbers of Vector-Valued Diagonal Operators
β Scribed by Eduard Belinsky
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 105 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0021-9045
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π SIMILAR VOLUMES
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 HardyαLittlewood maximal operator
## Abstract It is shown that a Banach space __E__ has type __p__ if and only for some (all) __d__ β₯ 1 the Besov space __B__^(1/__p__ β 1/2)__d__^ ~__p__,__p__~ (β^__d__^ ; __E__) embeds into the space __Ξ³__ (__L__^2^(β^__d__^ ), __E__) of __Ξ³__ βradonifying operators __L__^2^(β^__d__^ ) β __E__. A
The main purpose of this paper is to give some natural relations between the entropy numbers of an operator and those of its adjoint. This problem has attracted some recent attention (of. [ll], 14.3. 6 and[a]). Typically, we shall consider inequalities which allow a correction term. We obtain our fi