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Journal of the London Mathematical Society Advance Access published online on October 24, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm078
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© 2007 London Mathematical Society

An egg-yolk principle and exponential integrability for quasiregular mappings

Pietro Poggi-Corradini

Department of Mathematics
Cardwell Hall
Kansas State University
Manhattan
KS 66506
USA

Kai Rajala

Department of Mathematics and Statistics
University of Jyväskylä
PO Box 35 (MAD)
FIN-40014
Finland
kirajala@maths.jyu.fi

Quasiregular mappings f:{Omega}subRn->Rn are a natural generalization of analytic functions from complex analysis and provide a theory which is rich with new phenomena. In this paper we extend a well-known result of Chang and Marshall on exponential integrability of analytic functions in the disk, to the case of quasiregular mappings defined in the unit ball of Rn. To this end, an ‘egg-yolk’ principle is first established for such maps, which extends a recent result of the first author. Our work leaves open an interesting problem regarding n-harmonic functions.

2000 Mathematics Subject Classification 30C80, 30C65.

The second author was supported by the Academy of Finland. Part of this research was done when the second author was visiting the University of Cincinnati and the University of Michigan and the first author was visiting the University of Michigan. We wish to thank both departments for their hospitality.

Received November 12, 2006;
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