Outer functions in Qp#,  Qp,0#

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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Bibliographic Details
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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Summary: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#).
ISSN:0972-6802

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