An egg‐yolk principle and exponential integrability for quasiregular mappings

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.