On Bloch functions and gap series.

Daniel Girela

Publicacions Matemàtiques (1991)

  • Volume: 35, Issue: 2, page 403-427
  • ISSN: 0214-1493

Abstract

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Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general results obtaining sharp comparison results between the integral means Mp(r,f) with T(r,f) for certain classes of functions f analytic in the unit disc.

How to cite

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Girela, Daniel. "On Bloch functions and gap series.." Publicacions Matemàtiques 35.2 (1991): 403-427. <http://eudml.org/doc/41700>.

@article{Girela1991,
abstract = {Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general results obtaining sharp comparison results between the integral means Mp(r,f) with T(r,f) for certain classes of functions f analytic in the unit disc.},
author = {Girela, Daniel},
journal = {Publicacions Matemàtiques},
keywords = {BMOA; VMOA; Nevanlinna characteristic; Bloch space; Hadamard gaps},
language = {eng},
number = {2},
pages = {403-427},
title = {On Bloch functions and gap series.},
url = {http://eudml.org/doc/41700},
volume = {35},
year = {1991},
}

TY - JOUR
AU - Girela, Daniel
TI - On Bloch functions and gap series.
JO - Publicacions Matemàtiques
PY - 1991
VL - 35
IS - 2
SP - 403
EP - 427
AB - Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general results obtaining sharp comparison results between the integral means Mp(r,f) with T(r,f) for certain classes of functions f analytic in the unit disc.
LA - eng
KW - BMOA; VMOA; Nevanlinna characteristic; Bloch space; Hadamard gaps
UR - http://eudml.org/doc/41700
ER -

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