Brennan's conjecture for composition operators on Sobolev spaces

2012/12/17 by Vladimir Gol'dshtein, Alexander Ukhlov, Gol'dshtein, Vladimir +1
Mathematics · #30C62 #46E35 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C62 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1212.3999

8 pages

arxiv created 2013/02/14 · arxiv updated 2013/02/15

Abstract

We show that Brennan's conjecture is equivalent to boundedness of composition operators on homogeneous Sobolev spaces generated by conformal homeomorphisms of simply connected plane domains to the unit disc.

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