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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 920–930 (Mi smj2373)  

This article is cited in 14 scientific papers (total in 14 papers)

Estimation of the measure of the image of the ball

R. R. Salimov

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine

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.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 739–747

Bibliographic databases:

UDC: 517.5
Received: 24.05.2011
Revised: 30.12.2011

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

Citation in format AMSBIB
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\paper Estimation of the measure of the image of the ball
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\issue 4
\pages 920--930
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\issue 4
\pages 739--747
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. R. Salimov, “O koltsevykh $Q$-otobrazheniyakh otnositelno nekonformnogo modulya”, Dalnevost. matem. zhurn., 14:2 (2014), 257–269  mathnet
    2. R. R. Salimov, “Lower estimates of $p$-modulus and mappings of Sobolev's class”, St. Petersburg Math. J., 26:6 (2015), 965–984  mathnet  crossref  mathscinet  isi  elib  elib
    3. A. Golberg, R. Salimov, “Extension of the Schwarz lemma to homeomorphisms with controlled $p$-module”, Georgian Math. J., 21:3 (2014), 273–279  crossref  mathscinet  zmath  isi  elib  scopus
    4. E. S. Afanas'eva, “On the boundary behavior of one class of mappings in metric spaces”, Ukr. Math. J., 66:1 (2014), 16–29  crossref  mathscinet  zmath  isi  scopus
    5. A. Golberg, R. Salimov, “Logarithmic Hölder continuity of ring homeomorphisms with controlled $p$-module”, Complex Var. Elliptic Equ., 59:1, SI (2014), 91–98  crossref  mathscinet  zmath  isi  elib  scopus
    6. R. R. Salimov, “O konechnoi lipshitsevosti klassov Orlicha–Soboleva”, Vladikavk. matem. zhurn., 17:1 (2015), 64–77  mathnet
    7. A. Golberg, R. Salimov, E. Sevost'yanov, “Normal families of discrete open mappings with controlled $p$-module”, Complex Analysis and Dynamical Systems VI, v. 2, Contemporary Mathematics, 667, Complex Analysis, Quasiconformal Mappings, Complex Dynamics, eds. M. Agranovsky, M. Ben-Artzi, G. Galloway, L. Karp, D. Khavinson, S. Reich, G. Weinstein, L. Zalcman, Amer. Math. Soc., 2016, 83–103  crossref  mathscinet  zmath  isi
    8. R. R. Salimov, E. A. Sevost'yanov, “On Local Properties of Spatial Generalized Quasi-isometries”, Math. Notes, 101:4 (2017), 704–717  mathnet  crossref  crossref  mathscinet  isi  elib
    9. R. R. Salimov, B. A. Klischuk, “Ekstremalnaya zadacha dlya ploschadi obraza kruga”, Issledovaniya po lineinym operatoram i teorii funktsii. 45, Zap. nauchn. sem. POMI, 456, POMI, SPb., 2017, 160–171  mathnet
    10. A. Golberg, R. Salimov, “Hölder continuity of homeomorphisms with controlled growth of their spherical means”, Complex Anal. Oper. Theory, 11:8, SI (2017), 1825–1838  crossref  mathscinet  zmath  isi  scopus
    11. E. Afanas'eva, “Ring $Q$-homeomorphisms on Finsler manifolds”, Complex Anal. Oper. Theory, 11:7, SI (2017), 1557–1567  crossref  mathscinet  zmath  isi  scopus
    12. E. A. Sevostyanov, “O granichnom prodolzhenii i ravnostepennoi nepreryvnosti semeistv otobrazhenii v terminakh prostykh kontsov”, Algebra i analiz, 30:6 (2018), 97–146  mathnet
    13. E. A. Sevostyanov, “O granichnom povedenii nekotorykh klassov otobrazhenii”, Issledovaniya po lineinym operatoram i teorii funktsii. 46, Zap. nauchn. sem. POMI, 467, POMI, SPb., 2018, 169–190  mathnet
    14. Golberg A. Salimov R., “Regularity of Mappings With Integrally Restricted Moduli”, Complex Analysis and Dynamical Systems: New Trends and Open Problems, Trends in Mathematics, ed. Agranovsky M. Golberg A. Jacobzon F. Shoikhet D. Zalcman L., Birkhauser Verlag Ag, 2018, 129–140  crossref  mathscinet  zmath  isi  scopus
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