Brennan’s conjecture for composition operators on Sobolev spaces


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Authors

  • Vladimir Gol’dshtein
  • Alexander Ukhlov

Keywords:

Brennan’s conjecture, conformal mappings, composition operators, Sobolev spaces

Abstract

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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Published

2012-12-30

How to Cite

Gol’dshtein, V., & Ukhlov, A. (2012). Brennan’s conjecture for composition operators on Sobolev spaces. Eurasian Mathematical Journal, 3(4), 35–43. Retrieved from https://emj.enu.kz/index.php/main/article/view/805

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Section

Articles