On coefficients of vector-valued Bloch functions

• Autorzy: Oscar Blasco
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 165
• Numer: 2
• Strony: 101-110

Daty

wydano

2004

Twórcy

autor

Oscar Blasco

• Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain

Identyfikatory

DOI

10.4064/sm165-2-1