Integrability of derivatives of inverses of maps of exponentially integrable distortion in the plane

The K-quasiconformal maps form a category which is invariant under inversion, i.e. f and f −1 are simultaneously K-quasiconformal. Maps of exponentially integrable distortion are a useful class for extending the Beltrami equation to a degenerate setting. This class is not invariant under inversion. In this note we show that the inverses of homeomorphisms of exponentially p-integrable distortion have β-integrable distortion for all β < p , but not necessarily for β = p .