Results 51 to 60 of about 4,109,228 (193)

Fractional Derivative Description of the Bloch Space

Potential Analysis
AbstractWe establish new characterizations of the Bloch space $$\mathcal {B}$$ B which include descriptions in terms of classical fractional derivatives. Being precise, for an analytic function $$f(z)=\sum _{n=0}^\infty \widehat{f}(n) z^n$$ f (
Moreno, Álvaro Miguel, Peláez-Márquez, José Ángel, De la Rosa, Elena   +2 more
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The Bohr Radius of the Weighted Bloch Spaces

Lobachevskii Journal of Mathematics, 2023
The concept of the Bohr radius of a pair of Banach spaces is introduced. The lower estimate for the value of the Bohr radius from the Bloch space to the space of bounded functions obtained by I. Kayumov, S. Ponnusamy and N. Shakirov is slightly improved. It is shown that for any weighted Bloch space the Bohr radius is not less than $1/\sqrt{2}$.
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On Volterra composition operators from Bergman-type space to Bloch-type space [PDF]

, 2011
summary:Let $\varphi $ be an analytic self-mapping of $\mathbb {D}$ and $g$ an analytic function on $\mathbb {D}$. In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type ...
Jiang, Zhi Jie
core   +1 more source

The basic properties of Bloch functions

International Journal of Mathematics and Mathematical Sciences, 1979
A Bloch function f(z) is an analytic function on the unit disc 𝔻 whose derivative grows no faster than a constant times the reciprocal of the distance from z to ∂𝔻. We reprove here the basic analytic facts concerning Bloch functions.
Joseph A. Cima
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The composition operators on weighted Bloch space [PDF]

Archiv der Mathematik, 2002
Let \(H(D)\) denote the set of all holomorphic functions in the open unit disk \(D\) and let \(\phi\) be a holomorphic selfmap of \(D\). Suppose that \(X\) and \(Y\) are two function spaces defined on \(D\). The map \(\phi\) is said to have the \(X\)-to-\(Y\) pullback property if \(f\circ \phi\in Y\) for every \(f\in X\).
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Bloch, Adolpho -- 1972-92 -- Correspondence, Individual -- letter, 1972 - 1992?

, 1972
Letter from Bloch, Adolpho dated 1972 - 1992?.Sabin Collection Fair Use ...
Bloch, Adolpho, 1908-
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Characterizations of Bloch-Type Spaces of Harmonic Mappings

Journal of Function Spaces, 2019
We study the Banach space BHα (α>0) of the harmonic mappings h on the open unit disk D satisfying the condition supz∈D⁡(1-z2)α(hzz+hz¯z)0 the mappings in BHα can be characterized in terms of a Lipschitz condition relative to the metric defined by dH,α(z ...
Munirah Aljuaid, Flavia Colonna
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A problem on spaces of holomorphic maps and the geometry of image domains

Concrete Operators
We present an old problem in Geometric Function Theory: characterizing the domains Ω⊂C ${\Omega}\subset \mathbb{C}$ for which every holomorphic map from the unit disk into Ω must belong to a specific function space X.
Cruz-Zamorano Francisco J.
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Some characterizations of harmonic Bloch and Besov spaces [PDF]

, 2016
summary:The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega $-$\alpha $-Bloch space and characterize it in terms of $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\
Lu, Bowen, Fu, Xi
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Besov-type characterisations for the Bloch space [PDF]

Bulletin of the Australian Mathematical Society, 1989
We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space.
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