Exponential integrability of mappings of finite distortion

Abstract

We consider mappings with exponentially integrable distortion whose Jacobian determinants are integrable over the $n$-ball. We show that the boundary extensions of such mappings are exponentially integrable with bounds, and give examples to illustrate that there is not too much room for improvement. This extends the results of Beurling \[2], and Chang and Marshall \[3], \[10] on analytic functions, and Poggi-Corradini and Rajala \[14] on quasiregular mappings.