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On coefficients of vector-valued Bloch functions

Oscar Blasco — 2004

Studia Mathematica

Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc such that s u p | z | < 1 ( 1 - | z | ² ) | | f ' ( z ) | | < . A sequence (Tₙ)ₙ of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and ℓ₁(Y) if the map n = 0 x z ( T ( x ) ) defines a bounded linear operator from Bloch(X) into ℓ₁(Y). It is shown that if X is a Hilbert space then (Tₙ)ₙ is a multiplier from Bloch(X) into ℓ₁(Y) if and only if s u p k n = 2 k 2 k + 1 | | T | | ² < . Several results about Taylor coefficients of vector-valued...

Vector valued measures of bounded mean oscillation.

Oscar Blasco — 1991

Publicacions Matemàtiques

The duality between H1 and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained. In this paper we shall study such space in little more detail and we shall consider the H1-BMO duality for vector-valued functions in the more general setting of spaces of homogeneous type (see [CW]).

Summing multi-norms defined by Orlicz spaces and symmetric sequence space

Oscar Blasco — 2016

Commentationes Mathematicae

We develop the notion of the ( X 1 , X 2 ) -summing power-norm based on a Banach space E , where X 1 and X 2 are symmetric sequence spaces. We study the particular case when X 1 and X 2 are Orlicz spaces Φ and Ψ respectively and analyze under which conditions the ( Φ , Ψ ) -summing power-norm becomes a multinorm. In the case when E is also a symmetric sequence space L , we compute the precise value of ( δ 1 , , δ n ) n ( X 1 , X 2 ) where ( δ k ) stands for the canonical basis of L , extending known results for the ( p , q ) -summing power-norm based on the space r which...

Equivalences involving (p,q)-multi-norms

Oscar BlascoH. G. DalesHung Le Pham — 2014

Studia Mathematica

We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form L r ( Ω ) , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.

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