Abstract:
Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.
Keywords:p-modulus, p-capacity, Q-homeomorphism, ring Q-homeomorphism, quasiconformal mapping, mean quasiconformal mapping.
Citation:
R. R. Salimov, “Estimation of the measure of the image of the ball”, Sibirsk. Mat. Zh., 53:4 (2012), 920–930; Siberian Math. J., 53:4 (2012), 739–747
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\by R.~R.~Salimov
\paper Estimation of the measure of the image of the ball
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 4
\pages 920--930
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\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 4
\pages 739--747
\crossref{https://doi.org/10.1134/S0037446612040155}
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Linking options:
https://www.mathnet.ru/eng/smj2373
https://www.mathnet.ru/eng/smj/v53/i4/p920
This publication is cited in the following 33 articles:
Ruslan Salimov, Bogdan Klishchuk, Trends in Mathematics, New Tools in Mathematical Analysis and Applications, 2025, 89
Mariia V. Stefanchuk, “On exponential asymptotics of ring Q-homeomorphisms at infinity”, J Math Sci, 282:1 (2024), 83
V. Desyatka, E. Sevost'yanov, “Usuvnі singulyarnostі vіdobrazhen z obernenoyu nerіvnіstyu Poletskogo na rіmanovikh mnogovidakh”, Ukr. Mat. Zhurn., 76:7 (2024), 965
Mariia Volodymyrivna Stefanchuk, “On exponential asymptotics of one class of homeomorphisms at a point of the complex plane”, PIGC, 17:2 (2024), 158
Victoria Desyatka, Evgeny Sevost'yanov, “Removable Singularities of Mappings with Inverse Poletsky Inequality on Riemannian Manifolds”, Ukr Math J, 2024
Mariia V. Stefanchuk, “On exponential asymptotics of ring Q-homeomorphisms at infinity”, UMB, 21:1 (2024), 107
M.V. Stefanchuk, “On asymptotic behavior at infinity of lower Q-homeomorphisms with respect to p-modulus on the complex plane”, Proc. IAMM NASU, 38 (2024), 103
R. R. Salimov, V. A. Klishchuk, “On the Behavior of One Class of Homeomorphisms at Infinity”, Ukr Math J, 74:10 (2023), 1617
Igor Petkov, Ruslan Salimov, Mariia Stefanchuk, “On the distortion of the disk image diameter”, UMB, 20:2 (2023), 219
Miodrag Mateljevic, Evgeny Sevost'yanov, “On the behavior of Orlicz-Sobolev mappings with branching on the unit sphere”, UMB, 19:4 (2023), 541
Miodrag Mateljevic, Evgeny Sevost'yanov, “On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere”, J Math Sci, 270:3 (2023), 467
Evgeny Sevost'yanov, Developments in Mathematics, 78, Mappings with Direct and Inverse Poletsky Inequalities, 2023, 65
Bogdan Klishchuk, Ruslan Salimov, Mariia Stefanchuk, “On the asymptotic behavior at infinity of one mapping class”, PIGC, 16:1 (2023), 50
R. R. Salimov, B. A. Klishchuk, “Pro povedіnku odnogo klasu gomeomorfіzmіv na neskіnchennostі”, Ukr. Mat. Zhurn., 74:10 (2022), 1416
Bogdan A. Klishchuk, “On Power-Law Behavior of Some Mapping Class at Infinity”, J Math Sci, 268:2 (2022), 192
Ruslan Salimov, Bogdan Klishchuk, Trends in Mathematics, Current Trends in Analysis, its Applications and Computation, 2022, 173
Klishchuk B.A., Salimov R.R., “Lower Bounds For the Volume of the Image of a Ball”, Ukr. Math. J., 71:6 (2019), 883–895
Salimov R.R., Sevost'yanov E.A., Markish A.A., “on the Lower Estimate of the Distortion of Distance For One Class of Mappings”, Ukr. Math. J., 70:11 (2019), 1791–1802
E. A. Sevost'yanov, “On boundary extension and equicontinuity of families of mappings in terms of prime ends”, St. Petersburg Math. J., 30:6 (2019), 973–1005
E. A. Sevost'yanov, “On the boundary behavior of some classes of mappings”, J. Math. Sci. (N. Y.), 243:6 (2019), 934–948
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