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Rauno Aulaskari, Shamil Makhmutov, and Jouni Rättyä
Counterexamples on non-α-normal functions with good integrability view print
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| Published: |
January 30, 2011
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| Keywords: |
Dirichlet space, normal function, Blaschke product |
| Subject: |
Primary 30D50; Secondary 30D35, 30D45 |
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Abstract
Blaschke products are used to construct concrete examples of
analytic functions with good integrability and bad behavior of
spherical derivative. These examples are used to show that none of
the classes M#p, 0<p<∞, is contained in the
α-normal class Nα when 0<α<2. This implies that
M#p is in a sense a much larger class than Q#p.
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| Acknowledgements
This research was supported in part by the Academy of Finland #121281; IG/SCI//DOMS/10/04; MTM2007-30904-E, MTM2008-05891, MTM2008-02829-E (MICINN, Spain); FQM-210 (Junta de Andalucía, Spain); and the European Science Foundation RNP HCAA
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| Author information
Rauno Aulaskari:
University of Eastern Finland, Department of Physics and Mathematics, Campus of Joensuu, P. O. Box 111, 80101 Joensuu, Finland
rauno.aulaskari@uef.fi
Shamil Makhmutov:
Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al Khodh 123, Oman, UFA State Aviation Technical University, UFA, Russia
makhm@squ.edu.om
Jouni Rättyä:
University of Eastern Finland, Department of Physics and Mathematics, Campus of Joensuu, P. O. Box 111, 80101 Joensuu, Finland
jouni.rattya@uef.fi
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