Markov inequality on the graph of holomorphic function

2017 ◽  
Vol 1 (1) ◽  
pp. 58-64
Author(s):  
Tomasz Beberok
Keyword(s):  
Holomorphic Function ◽  
Markov Inequality

The purpose of this paper is to show that the Markov inequality does not hold on the graph of holomorphic function.

scholarly journals A Criterion for Normalcy

1968 ◽  
Vol 32 ◽  
pp. 277-282 ◽  
Author(s):  
Paul Gauthier
Keyword(s):  
Meromorphic Function ◽  
Holomorphic Function ◽  
Unit Disc ◽  
Meromorphic Functions

Gavrilov [2] has shown that a holomorphic function f(z) in the unit disc |z|<1 is normal, in the sense of Lehto and Virtanen [5, p. 86], if and only if f(z) does not possess a sequence of ρ-points in the sense of Lange [4]. Gavrilov has also obtained an analagous result for meromorphic functions by introducing the property that a meromorphic function in the unit disc have a sequence of P-points. He has shown that a meromorphic function in the unit disc is normal if and only if it does not possess a sequence of P-points.

A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

2012 ◽  
Vol 55 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Songxiao Li ◽  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

scholarly journals On the Relation between a Cluster set Introduced by Constantinescu and Cornea, and the Fine Cluster set of Cartan, Brelot, and Naïm

1965 ◽  
Vol 8 (1) ◽  
pp. 59-71
Author(s):  
H. L. Jackson
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Limit Theorems ◽  
Function Theory ◽  
Angular Limit ◽  
Boundary Limit ◽  
Cluster Set ◽  
Almost Everywhere ◽  
Bounded Holomorphic Function ◽  
Bounded Holomorphic

The field of boundary limit theorems in analytic function theory is usually considered to have begun about 1906, with the publication of Fatou's thesis [8]. In this remarkable memoir a theorem is proved, that now bears the author's name, which implies that any bounded holomorphic function defined on the unit disk possesses an angular limit almost everywhere (Lebesgue measure) on the frontier. Outstanding classical contributions to this field can be attributed to F. and M. Riesz, R. Nevanlinna, Lusin, Privaloff, Frostman, Plessner, and others.

p-Radial Exceptional Sets and Conformal Mappings

2007 ◽  
Vol 50 (4) ◽  
pp. 579-587
Author(s):  
Piotr Kot
Keyword(s):  
Holomorphic Function ◽  
Unit Disc ◽  
Conformal Mappings ◽  
Exceptional Sets ◽  
Image Position

AbstractFor p > 0 and for a given set E of type Gδ in the boundary of the unit disc ∂ we construct a holomorphic function f ∈ such thatIn particular if a set E has a measure equal to zero, then a function f is constructed as integrable with power p on the unit disc .

Sign in / Sign up

Export Citation Format

Share Document