Outer functions in Qp#,  Qp,0#

For 0<p<∞,  Qp#  (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying sup⁡w∈D∬D(f#(z))2gp(z,w)dσz<∞  (lim⁡w→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp#  (Qp,0#) are given by the...

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Main Authors: Rauno Aulaskari, Hasi Wulan
Format: Article
Language:English
Published: Wiley 2004-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2004/493269
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author Rauno Aulaskari
Hasi Wulan
author_facet Rauno Aulaskari
Hasi Wulan
author_sort Rauno Aulaskari
collection DOAJ
description For 0<p<∞,  Qp#  (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying sup⁡w∈D∬D(f#(z))2gp(z,w)dσz<∞  (lim⁡w→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp#  (Qp,0#) are given by the Ahlfors-Shimizu characteristic. Further, outer functions in Qp#  (Qp,0#) are characterized and shown that every function in Qp#  (Qp,0#) can be represented as the quotient of two functions in H∞∩Qp#  (H∞∩Qp,0#).
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spelling doaj-art-0d042553616a45839b40870ea9dda10d2025-08-20T02:03:04ZengWileyJournal of Function Spaces and Applications0972-68022004-01-0121172410.1155/2004/493269Outer functions in Qp#,  Qp,0#Rauno Aulaskari0Hasi Wulan1Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, FinlandDepartment of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, FinlandFor 0<p<∞,  Qp#  (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying sup⁡w∈D∬D(f#(z))2gp(z,w)dσz<∞  (lim⁡w→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp#  (Qp,0#) are given by the Ahlfors-Shimizu characteristic. Further, outer functions in Qp#  (Qp,0#) are characterized and shown that every function in Qp#  (Qp,0#) can be represented as the quotient of two functions in H∞∩Qp#  (H∞∩Qp,0#).http://dx.doi.org/10.1155/2004/493269
spellingShingle Rauno Aulaskari
Hasi Wulan
Outer functions in Qp#,  Qp,0#
Journal of Function Spaces and Applications
title Outer functions in Qp#,  Qp,0#
title_full Outer functions in Qp#,  Qp,0#
title_fullStr Outer functions in Qp#,  Qp,0#
title_full_unstemmed Outer functions in Qp#,  Qp,0#
title_short Outer functions in Qp#,  Qp,0#
title_sort outer functions in qp qp 0
url http://dx.doi.org/10.1155/2004/493269
work_keys_str_mv AT raunoaulaskari outerfunctionsinqpqp0
AT hasiwulan outerfunctionsinqpqp0