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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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2015-01-01
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Series: | Journal of Function Spaces |
Online Access: | http://dx.doi.org/10.1155/2015/376089 |
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). |
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ISSN: | 2314-8896 2314-8888 |