Convolution of Operators and Applications.
On the dual space of
Interpolation between and
On coefficients of vector-valued Bloch functions
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 . 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 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 . Several results about Taylor coefficients of vector-valued...
A class of operators from a Banach lattice into a Banach space.
Vector valued measures of bounded mean oscillation.
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
We develop the notion of the -summing power-norm based on a Banach space , where and are symmetric sequence spaces. We study the particular case when and are Orlicz spaces and respectively and analyze under which conditions the -summing power-norm becomes a multinorm. In the case when is also a symmetric sequence space , we compute the precise value of where stands for the canonical basis of , extending known results for the -summing power-norm based on the space which...
The Bergman projection on weighted spaces: L¹ and Herz spaces
We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces .
Non interpolation in Morrey-Campanato and block spaces
Hardy spaces of Banach-space-valued functions depending on the geometry of the Banach space.
The purpose of this note is to announce some results related to Hardy spaces of vector valued functions and to show that some properties on B have to be required if we want that the classical theorems to remain valid in the B-valued setting.
On the Bloch space and convolution of functions in the Lp-valued case.
Dimension free estimates for the bilinear Riesz transform.
On functions of integrable mean oscillation.
Lp continuity of projectors of weighted harmonic Bergman spaces.
Algebras de Banach de medidas vectoriales.
Bilinear multipliers and transference.
Equivalences involving (p,q)-multi-norms
We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form , 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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