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An egg‐yolk principle and exponential integrability for quasiregular mappings
Author(s) -
Poggi-Corradini Pietro,
Rajala Kai
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm078
Subject(s) - generalization , exponential function , mathematics , analytic function , yolk , pure mathematics , harmonic function , mathematical analysis , chemistry , food science
Quasiregular mappings f :Ω⊂ℝ n →ℝ n 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 ℝ n . 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.