Page 1

Displaying 1 – 16 of 16

Showing per page

A formula for the Bloch norm of a C 1 -function on the unit ball of n

Miroslav Pavlović (2008)

Czechoslovak Mathematical Journal

For a C 1 -function f on the unit ball 𝔹 n we define the Bloch norm by f 𝔅 = sup d ˜ f , where d ˜ f is the invariant derivative of f , and then show that f 𝔅 = sup z , w 𝔹 z w ( 1 - | z | 2 ) 1 / 2 ( 1 - | w | 2 ) 1 / 2 | f ( z ) - f ( w ) | | w - P w z - s w Q w z | .

Bloch-to-Hardy composition operators

Evgueni Doubtsov, Andrei Petrov (2013)

Open Mathematics

Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.

Holomorphic Bloch spaces on the unit ball in C n

A. V. Harutyunyan, Wolfgang Lusky (2009)

Commentationes Mathematicae Universitatis Carolinae

This work is an introduction to anisotropic spaces of holomorphic functions, which have ω -weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding L ω space. We establish a description of ( A p ( ω ) ) * via the Bloch classes for all 0 < p 1 .

On some inequalities in holomorphic function theory in polydisk related to diagonal mapping

Romi F. Shamoyan, Olivera R. Mihić (2010)

Czechoslovak Mathematical Journal

We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.

On spaces of holomorphic functions in ℂⁿ

Diana D. Jiménez S., Lino F. Reséndis O., Luis M. Tovar S. (2014)

Banach Center Publications

Following the line of Ouyang et al. (1998) to study the p spaces of holomorphic functions in the unit ball of ℂⁿ, we present in this paper several results and relations among p ( ) , the α-Bloch, the Dirichlet p and the little p , 0 spaces.

Some characterizations of harmonic Bloch and Besov spaces

Xi Fu, Bowen Lu (2016)

Czechoslovak Mathematical Journal

The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic ω - α -Bloch space and characterize it in terms of ω ( ( 1 - | x | 2 ) β ( 1 - | y | 2 ) α - β ) | f ( x ) - f ( y ) x - y | and ω ( ( 1 - | x | 2 ) β ( 1 - | y | 2 ) α - β ) | f ( x ) - f ( y ) | x | y - x ' | where ω is a majorant. Similar results are extended to harmonic little ω - α -Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).

The Bloch space for the minimal ball

G. Mengotti (2001)

Studia Mathematica

We introduce the Bloch space for the minimal ball and we prove that this space can be identified with the dual of a certain analytic space which is strongly related to the Bergman theory on the minimal ball.

The Lindelöf principle in ℂn

Peter Dovbush (2013)

Open Mathematics

Let D be a bounded domain in ℂn. A holomorphic function f: D → ℂ is called normal function if f satisfies a Lipschitz condition with respect to the Kobayashi metric on D and the spherical metric on the Riemann sphere ̅ℂ. We formulate and prove a few Lindelöf principles in the function theory of several complex variables.

Un théorème de Bloch presque complexe

Benoît Saleur (2014)

Annales de l’institut Fourier

Cet article est consacré à la démonstration d’une version presque complexe du théorème de Bloch. Considérons la réunion C de quatre J-droites en position générale dans un plan projectif presque complexe. Nous démontrons que toute suite non normale de J-disques évitant évitant la configuration C admet une sous-suite convergeant, au sens de Hausdorff, vers une partie la réunion des diagonales de C. En particulier, le complémentaire de la configuration C est hyperboliquement plongé dans le paln projectif...

Currently displaying 1 – 16 of 16

Page 1