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On Orlicz–Sobolev Classes on Quotient Spaces

Abstract

We study the quotient spaces of the unit ball by some group of Möbius transformations. For mappings of such spaces, we obtain a bound for the distortion of a modulus of a family of spheres. As an application, we prove theorems on the local and boundary behavior of Orlicz–Sobolev classes on the quotient spaces.

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Correspondence to E. A. Sevost’yanov.

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Sevost’yanov, E.A. On Orlicz–Sobolev Classes on Quotient Spaces. Sib. Adv. Math. 31, 209–228 (2021). https://doi.org/10.1134/S1055134421030044

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Keywords

  • mappings with finite and bounded distortion
  • local and boundary behavior of mappings
  • moduli of families of curves.