scholarly journals Mean growth of the derivative of analytic functions bounded mean oscillation and normal functions

1998 ◽  
Vol 47 (3) ◽  
pp. 0-0 ◽  
Author(s):  
Oscar Blasco ◽  
Daniel Girela ◽  
M. A. Marquez
Keyword(s):  
Analytic Functions ◽  
Bounded Mean Oscillation ◽  
Normal Functions ◽  
Mean Oscillation

On Analytic Functions of Bergman BMO in the Ball

1999 ◽  
Vol 42 (1) ◽  
pp. 97-103 ◽  
Author(s):  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bounded Mean Oscillation ◽  
Open Unit ◽  
Bergman Metric ◽  
Open Unit Ball ◽  
Mean Oscillation ◽  
Volume Measure

AbstractLet B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for whichif 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.

scholarly journals On M-ideals and o-O type spaces

2017 ◽  
Vol 121 (1) ◽  
pp. 151 ◽  
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Type Spaces ◽  
Invariant Spaces ◽  
Holder Spaces ◽  
Spaces Of Analytic Functions

We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.

scholarly journals Characterisations for analytic functions of bounded mean oscillation

1992 ◽  
Vol 46 (1) ◽  
pp. 115-125 ◽  
Author(s):  
Jie Miao
Keyword(s):  
Analytic Function ◽  
Fractional Derivative ◽  
Lebesgue Measure ◽  
Analytic Functions ◽  
Unit Disc ◽  
Carleson Measure ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Significant Extension

Let α > 0 and let f[α](z) be the αth fractional derivative of an analytic function f on the unit disc D. In this paper we show that f ∈ BMOA if and only if |f[α](z)|2 (l - |z|2)2α−1dA(z) is a Carleson measure and f ∈ VMOA if and only if |f[α](z)|2 (1 − |z|2)2α−1dA(z) is a vanishing Carleson measure, where A denotes the normalised Lebesgue measure on D. Hence a significant extension of familiar characterisations for analytic functions of bounded and vanishing mean oscillation is obtained.

Range Sets And Bmo Norms of Analytic Functions

1984 ◽  
Vol 36 (4) ◽  
pp. 747-755 ◽  
Author(s):  
Shoji Kobayashi
Keyword(s):  
Riemann Surface ◽  
Analytic Function ◽  
Green's Function ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Bounded Mean Oscillation ◽  
Open Riemann Surface ◽  
Mean Oscillation ◽  
Image Position ◽  
Dirichlet Integrals

In this paper we are concerned with the space BMOA of analytic functions of bounded mean oscillation for Riemann surfaces, and it is shown that for any analytic function on a Riemann surface the area of its range set bounds the square of its BMO norm, from which it is seen as an immediate corollary that the space BMOA includes the space AD of analytic functions with finite Dirichlet integrals.Let R be an open Riemann surface which possesses a Green's function, i.e., R ∉ OG, and f b e an analytic function defined on R. The Dirichletintegral DR(f) = D(f) of f on R is defined by1.1and we denote by AD(R) the space of all functions f analytic on R for which D(f) < +∞.

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