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On the compactification of classes with integral constrains on the Lavrent'ev characteristic

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Literature Cited

  1. M. A. Lavrent'ev, “Sur une classe de representations continues,” Mat. Sb.,42, No. 4, 407–423 (1935).

    Google Scholar 

  2. V. Ya. Gutlyanskii and V. I. Ryazanov, “On quasiconformal mappings with integral constraints on the M. A. Lavrent'ev characteristic,” Sib. Mat. Zh.,31, No. 2, 21–36 (1990).

    Google Scholar 

  3. N. Burbaki (N. Bourbaki), Functions of a Real Variable [Russian translation], Nauka, Moscow (1965).

    Google Scholar 

  4. V. I. Ryazanov, “On the closure of quasiconformal mappings with integral constraints,” Preprint No. 90.04, IPMM, Akad. Nauk Ukrainsk. SSSR, Donetsk (1990).

    Google Scholar 

  5. R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton (1970).

    Google Scholar 

  6. M. A. Krasnosel'skii and Ya. B. Rutitskii (Ya. B. Rutickii), Convex Functions and Orlicz Spaces, Noordhoff, Groningen (1961).

    Google Scholar 

  7. S. Saks, Theory of the Integral, Dover, New York (1964).

    Google Scholar 

  8. M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden (1976).

    Google Scholar 

  9. K. Strebel, “Ein Konvergenzsatz für Folgen quasikonformer Abbildungen,” Comment. Math. Helv.,44, 469–475 (1969).

    Google Scholar 

  10. O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Springer, Berlin (1965).

    Google Scholar 

  11. K. Leschinger, Untersuchungen über Jacobi-Determinanten von zweidimensionalen quasikonformen Abbildungen, Doctoral Dissertation, Bonner Math. Schriften, No. 72 (1974).

  12. H. Renelt, Quasikonforme Abbildungen und Elliptische Systeme Erster Ordnung in der Ebene, Teubner, Leipzig (1982).

    Google Scholar 

  13. V. I. Ryazanov, “On convergence of characteristics of quasiconformal mappings,” Ukr. Mat. Zh.,38, No. 2, 200–204 (1986).

    Google Scholar 

  14. V. I. Ryazanov, “On necessary and sufficient condition for convergence of complex dilatations,” Pliska Stud. Math. Bulgar.,10, 39–44 (1989).

    Google Scholar 

  15. P. S. Uryson (P. Urysohn), “Sur les classes (L) de M. Fréchet,” Enseign. Math.,25, 77–83 (1926).

    Google Scholar 

  16. P. S. Uryson, Works on Topology and Other Fields of Mathematics, Vol. II [in Russian], GITTL, Moscow (1951).

    Google Scholar 

  17. K. Kuratowski, Topology, Vol. I, Academic Press, New York (1966).

    Google Scholar 

  18. V. I. Ryazanov, “Some questions of convergence and compactness for quasiconformal mappings,” in: Theory of Mappings and Approximation of Functions [in Russian], Naukova Dumka, Kiev (1983), pp. 50–62.

    Google Scholar 

  19. V. I. Ryazanov, “Some questions of convergence and compactness for quasiconformal mappings,” Amer. Math. Soc. Translations, Series 2,131, 7–19 (1986).

    Google Scholar 

  20. V. I. Ryazanov, “Convergence and compactness theorems for quasiconformal mappings, and their applications,” Author's Abstract of Candidate's Dissertation, Donetsk (1983).

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Donetsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 87–104, January–February, 1992.

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Ryazanov, V.I. On the compactification of classes with integral constrains on the Lavrent'ev characteristic. Sib Math J 33, 70–86 (1992). https://doi.org/10.1007/BF00972939

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  • DOI: https://doi.org/10.1007/BF00972939

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