New York Journal of Mathematics
Volume 17a (2011) 165-175

Volume 17a

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Rauno Aulaskari, Shamil Makhmutov, and Jouni Rättyä

Counterexamples on non-α-normal functions with good integrability

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Published: January 30, 2011
Keywords: Dirichlet space, normal function, Blaschke product
Subject: Primary 30D50; Secondary 30D35, 30D45
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.
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
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