Necessary and Sufficient Conditions for Inner Functions to Be in QK(p,p-2)-Spaces

Under some regularity conditions on K, inner functions in QK(p,p-2)-spaces are characterized in the following way: an inner function belongs to QK(p,p-2) if and only if it is a Blaschke product associated with {zn} satisfying supa∈D∑nK(1-|φa(zn)|)<∞, where φa(z)=(a-z)/(1-a¯z). The result generali...

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Bibliographic Details
Main Author: Atte Reijonen
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2015/376089
Description
Summary:Under some regularity conditions on K, inner functions in QK(p,p-2)-spaces are characterized in the following way: an inner function belongs to QK(p,p-2) if and only if it is a Blaschke product associated with {zn} satisfying supa∈D∑nK(1-|φa(zn)|)<∞, where φa(z)=(a-z)/(1-a¯z). The result generalizes earlier theorems in (Essén et al., 2006) and (Pérez-González and Rättyä, 2009).
ISSN:2314-8896
2314-8888