Wyniki wyszukiwania

1

On coefficients of vector-valued Bloch functions

100%

Blasco O.

Studia Mathematica

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2004

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tom 165

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nr 2

101-110

EN

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 $sup_{|z|<1} (1 - |z|²)||f'(z)|| < ∞$. 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 $∑_{n=0}^{∞} xₙzⁿ → (Tₙ(xₙ))ₙ$ 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 $sup_{k} ∑_{n=2^{k}}^{2^{k+1}} ||Tₙ||² < ∞$. Several results about Taylor coefficients of vector-valued Bloch functions depending on properties on X, such as Rademacher and Fourier type p, are presented.

2

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

100%

Blasco O.

Commentationes Mathematicae

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2016

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tom 56

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nr 1

EN

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 $\ell_\Phi$ and $\ell_\Psi$ respectively and analyze under which conditions the $(\Phi, \Psi)$-summing power-norm becomes a~multinorm. In the case when $E$ is also a~symmetric sequence space $L$, we compute the precise value of $\|(\delta_1,\cdots,\delta_n)\|_n^{(X_1,X_2)}$ where $(\delta_k)$ stands for the canonical basis of $L$, extending known results for the $(p,q)$-summing power-norm based on the space $\ell_r$ which corresponds to $X_1=\ell_p$, $X_2=\ell_q$, and $E=\ell_r$.

3

The Bergman projection on weighted spaces: L¹ and Herz spaces

64%

Blasco O., Pérez-Esteva S.

Studia Mathematica

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2002

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tom 150

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nr 2

151-162

EN

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 $K_{p}^{q}(w)$.

4

Equivalences involving (p,q)-multi-norms

51%

Blasco O., Dales H., Pham H.

Studia Mathematica

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2014

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tom 225

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nr 1

29-59

EN

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.

5

On the dual space of $H^{1,∞}_B$

32%

Blasco O.

Colloquium Mathematicum

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1988

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tom 55

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nr 2

253-259

6

Interpolation between $H^{1}_{B_{0}}$ and $L^{P}_{B_{1}}$

32%

Blasco O.

Studia Mathematica

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1989

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tom 92

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nr 3

205-210

Ograniczanie wyników

4 Studia Mathematica

1 Colloquium Mathematicum

1 Commentationes Mathematicae

6 Blasco O.

1 Dales H.

1 Pham H.

1 Pérez-Esteva S.

1 2016

1 2014

1 2004

1 2002

1 1989

1 1988

On coefficients of vector-valued Bloch functions

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

The Bergman projection on weighted spaces: L¹ and Herz spaces

Equivalences involving (p,q)-multi-norms

On the dual space of $H^{1,∞}_B$

Interpolation between $H^{1}_{B_{0}}$ and $L^{P}_{B_{1}}$