On boundary behavior of mappings with two normalized conditions

Author
E. A. Sevost’yanov1, S. A. Skvortsov2, N. S. Ilkevych3
1) Zhytomyr Ivan Franko State University Zhytomyr, Ukraine; 2) Zhytomyr Ivan Franko State University Zhytomyr, Ukraine; 3) Zhytomyr Ivan Franko State University Zhytomyr, Ukraine
Abstract
The paper is devoted to a study of mappings with finite distortion that have been recently actively investigated last time. We study the boundary behavior of mappings between two fixed domains in metric spaces, which satisfy some moduli estimates. We have proved that families of corresponding inverse mappings with two normalized conditions and integrable majorant are equicontinuous whenever the domain of the mappings has a weakly at boundary
Keywords
metric spaces; quasiconformal mappings; mappings with bounded and finite distortion; equicontinuity; moduli of families of paths
DOI
doi:10.15330/ms.49.2.150-157
Reference
1. E. A. Sevost’yanov, S. A. Skvortsov, On convergence of mappings in metric spaces with direct and inverse modulus conditions, Ukr. Math. Zh., 70 (2018), ¹7, 952–967. (in Russian)

2. O. Martio, V. Ryazanov, U. Srebro and E. Yakubov, Moduli in Modern Mapping Theory, Springer Monographs in Mathematics, Springer, New York etc., 2009.

3. V. Ryazanov, R. Salimov, Weakly flat spaces and boundaries in the mapping theory, Ukr. Math. Visnyk, 4 (2007), ¹2, 199–233 (in Russian); translation in Ukr. Math. Bull., 4 (2007), ¹2, 199–233.

4. E. S. Smolovaya, Boundary behavior of ring Q-homeomorphisms in metric spaces, Ukr. Mat. Zh., 62 (2010), ¹5, 682–689 (in Russian); translation in Ukr. Math. Journ., 62 (2010), ¹5, 785–793.

5. K. Kuratowski, Topology, V.2, Academic Press, New York–London, 1968.

6. E. A. Sevost’yanov, On local and boundary behavior of mappings in metric spaces, Algebra and analiz 28 (2016), ¹6, 118–146; translation Local and boundary behavior of maps in metric spaces, St. Petersburg Math. J., 28 (2017), ¹6, 807–824.

7. M. Vuorinen, On the existence of angular limits of n-dimensional quasiconformal mappings, Ark. Mat., 18 (1980), 157–180.

8. E. A. Sevost’yanov, R. R. Salimov, On inner dilatations of the mappings with unbounded characteristic, Ukr. Mat. Visnyk, 8 (2011), ¹1, 129–143 (in Russian); translation in J. Math. Sci. (N. Y.), 178 (2011), ¹1, 97–107.

Pages
150-157
Volume
49
Issue
2
Year
2018
Journal
Matematychni Studii
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