Homeomorphisms of Finite Inner Distortion: Composition Operators on Zygmund-Sobolev and Lorentz-Sobolev Spaces
Let p > n-1 and αR and suppose that f:Ωonto Ω^′ is a homeomorphism in the Zygmund-Sobolev space WL^p^α L_loc olimits (Ω,R^n). Define r=p p-n+1. Assume that uWL^r^-α(r-1) L_loc olimits(Ω). Then u°f^-1 BV_loc olimits(Ω^′). We obtain a similar result whenever f is a homeomorphism in the Lorentz-Sobolev space WL^p,q_loc olimits (Ω,R^n) with p,q>n-1 and uWL^r,s_loc olimits(Ω) with r as before and s=q q-n+1. Moreover, if we further assume that f has finite inner distortion we obtain in both cases u° f^-1 W^1,1_loc olimits(Ω^′). , number=1, journal=MATHEMATICA SCANDINAVICA, author=Farroni, F. and Giova, R. and Moscariello, G. and Schiattarella, R., year=2015, month=Mar., pages=34–52