An egg-yolk principle and exponential integrability for quasiregular mappings

الأصل · EN

Quasiregular mappings f:Ω⊂ⁿ→ 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 A. Chang and D. Marshall on exponential integrability of analytic functions in the disk, to the case of quasiregular mappings defined in the unit ball of ⁿ. To this end, we first establish an ``egg-yolk'' principle for such maps, which extends a recent result of the first author. Our work leaves open an interesting problem regarding n-harmonic functions.