On Orlicz–Sobolev Classes on Quotient Spaces

被引：0
作者：
Sevost’yanov E.A. [1 ,2 ]
机构：
[1] Zhytomyr Ivan Franko State University, Zhytomyr
[2] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk
来源：
Siberian Advances in Mathematics | 2021年 / 31卷 / 3期
关键词：
local and boundary behavior of mappings; mappings with finite and bounded distortion; moduli of families of curves;
D O I：
10.1134/S1055134421030044
中图分类号：
学科分类号：
摘要：
Abstract: We study the quotient spaces of the unit ball by some group of Möbiustransformations. For mappings of such spaces, we obtain a bound for the distortion of a modulusof a family of spheres. As an application, we prove theorems on the local and boundary behaviorof Orlicz–Sobolev classes on the quotient spaces. © 2021, Pleiades Publishing, Ltd.
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页码：209 / 228
页数：19
相关论文
共 40 条
  • [1] Apanasov B.N., Geometry of Discrete Groups and Manifolds, (1991)
  • [2] Apanasov B., Topological barriers for locally homeomorphic quasiregular mappings in 3-space, Ann. Acad. Sci. Fenn. Math., 43, (2018)
  • [3] Calderon A.P., On the differentiability of absolutely continuous functions, Riv. Math. Univ. Parma, 2, (1951)
  • [4] Cristea M., Local homeomorphisms having local $$ACL^n$$ inverses, Complex Var. Elliptic Equ., 53, (2008)
  • [5] Federer H., Geometric Measure Theory, (1969)
  • [6] Fuglede B., Extremal length and functional completion, Acta Math., 98, (1957)
  • [7] Gehring F.-W., Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc., 103, (1962)
  • [8] Gol'dshtein V., Ukhlov A., Traces of functions of $$L^1_2$$ Dirichlet spaces on the Carathéodory boundary, Stud. Math., 235, 3, (2016)
  • [9] Greshnov A.V., Local approximation of uniformly regular Carnot–Carathéodory quasispaces by their tangent cones, Sib. Math. J., 48, (2007)
  • [10] Gutlyanskii V.Y., Ryazanov V.I., Yakubov E., The Beltrami equations and prime ends, J. Math. Sci., 210, (2015)
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