Geodesic
Brennan's conjecture for composition operators on Sobolev spaces
Eurasian mathematical journal, Tome 3 (2012) no. 4, pp. 35-43

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We show that Brennan's conjecture is equivalent to the boundedness of composition operators on homogeneous Sobolev spaces, that are generated by conformal homeomorphisms of simply connected plane domains to the unit disc. A geometrical interpretation of Brennan's conjecture in terms of integrability of $p$-distortion is given. 
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     author = {V. Gol'dshtein and A. Ukhlov},
     title = {Brennan's conjecture for composition operators on {Sobolev} spaces},
     journal = {Eurasian mathematical journal},
     pages = {35--43},
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     number = {4},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a3/}
}
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V. Gol'dshtein; A. Ukhlov. Brennan's conjecture for composition operators on Sobolev spaces. Eurasian mathematical journal, Tome 3 (2012) no. 4, pp. 35-43. http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a3/