Records 
Author 
Galanopoulos, P.; Girela, D.; Hernandez, R. 
Title 
Univalent Functions, VMOA and Related Spaces 
Type 

Year 
2011 
Publication 
Journal Of Geometric Analysis 
Abbreviated Journal 
J. Geom. Anal. 
Volume 
21 
Issue 
3 
Pages 
665682 
Keywords 
Univalent functions; VMOA; Bloch function; Besov spaces; Logarithmic Bloch spaces; Logarithmic derivative; Schwarzian derivative; Smooth Jordan curve 
Abstract 
This paper is concerned mainly with the logarithmic Bloch space B(log) which consists of those functions f which are analytic in the unit disc D and satisfy sup(z<1)(1z) log 1/1z f' (z)<infinity, and the analytic Besov spaces Bp, 1 <= p < infinity. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We give explicit examples of: A bounded univalent function in U(p>1) B(P) Bp but not in the logarithmic Bloch space. A bounded univalent function in B(log) but not in any of the Besov spaces B(p) with p < 2. We also prove that the situation changes for certain subclasses of univalent functions. Namely, we prove that the convex univalent functions in D which belong to any of the spaces B(0), VMOA, B(p) (1 <= p <= infinity), Blog, or some other related spaces are the same, the bounded ones. We also consider the question of when the logarithm of the derivative, log g', of a univalent function g belongs to Besov spaces. We prove that no condition on the growth of the Schwarzian derivative Sg of g guarantees log g' is an element of B(p). On the other hand, we prove that the condition integral(D) (1z(2))(2p2) Sg(z)(p) d A(z)<infinity implies that log g' is an element of B(p) and that this condition is sharp. We also study the question of finding geometric conditions on the image domain g(D) which imply that log g' lies in Bp. First, we observe that the condition of g( D) being a convex Jordan domain does not imply this. On the other hand, we extend results of Pommerenke and Warschawski, obtaining for every p is an element of (1, infinity), a sharp condition on the smoothness of a Jordan curve Gamma which implies that if g is a conformal mapping from D onto the inner domain of Gamma, then log g' is an element of B(p). 
Address 
[Galanopoulos, P; Girela, D] Univ Malaga, Fac Ciencias, Dept Anal Matemat, E29071 Malaga, Spain, Email: galanopoulos_petros@yahoo.gr 
Corporate Author 

Thesis 

Publisher 
Springer 
Place of Publication 

Editor 

Language 
English 
Summary Language 

Original Title 

Series Editor 

Series Title 

Abbreviated Series Title 

Series Volume 

Series Issue 

Edition 

ISSN 
10506926 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000291745600009 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
154 
Permanent link to this record 



Author 
Efraimidis, I.; Gaona, J.; Hernandez, R.; Venegas, O. 
Title 
On harmonic Blochtype mappings 
Type 

Year 
2017 
Publication 
Complex Variables And Elliptic Equations 
Abbreviated Journal 
Complex Var. Elliptic Equ. 
Volume 
62 
Issue 
8 
Pages 
10811092 
Keywords 
Bloch functions; harmonic functions; Jacobian; univalent functions; schlicht radius; growth estimates; coefficient estimates; 30C25; 30C50; 30D45; 30H30 
Abstract 
Let f be a complexvalued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Blochtype function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the wellknown analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent. 
Address 
[Efraimidis, I.] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain, Email: iason.efraimidis@uam.es 
Corporate Author 

Thesis 

Publisher 
Taylor & Francis Ltd 
Place of Publication 

Editor 

Language 
English 
Summary Language 

Original Title 

Series Editor 

Series Title 

Abbreviated Series Title 

Series Volume 

Series Issue 

Edition 

ISSN 
17476933 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000399938900004 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
729 
Permanent link to this record 



Author 
Bravo, V.; Hernandez, R.; Venegas, O. 
Title 
On the univalence of certain integral for harmonic mappings 
Type 

Year 
2017 
Publication 
Journal Of Mathematical Analysis And Applications 
Abbreviated Journal 
J. Math. Anal. Appl. 
Volume 
455 
Issue 
1 
Pages 
381388 
Keywords 
Harmonic mapping; Univalent functions; Integral transform 
Abstract 
We generalize the problem of univalence of the integral of f'(z)(alpha) when f is univalent to the complex harmonic mappings. To do this, we extend the univalence criterion by Ahlfors in [1] to those mappings. (C) 2017 Elsevier Inc. All rights reserved. 
Address 
[Bravo, Victor] Univ Valparaiso, Inst Matemat, Fac Ciencias, Valparaiso, Chile, Email: victor.bravo@uv.cl; 
Corporate Author 

Thesis 

Publisher 
Academic Press Inc Elsevier Science 
Place of Publication 

Editor 

Language 
English 
Summary Language 

Original Title 

Series Editor 

Series Title 

Abbreviated Series Title 

Series Volume 

Series Issue 

Edition 

ISSN 
0022247x 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000424735900019 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
826 
Permanent link to this record 