|
|
|
References
|
|
|
1. |
Afanaseva E. S., Ryazanov V. I., Salimov R. R., “Ob otobrazheniyakh klassa Orlicha–Soboleva na rimanovykh mnogoobraziyakh”, Ukr. mat. vestn., 8:3 (2011), 319–342 |
2. |
Vodopyanov S. K., “Otobrazheniya s ogranichennym iskazheniem i s konechnym iskazheniem na gruppakh Karno”, Sib. mat. zh., 40:4 (1999), 764–804 |
3. |
Vodopyanov S. K., Goldshtein V. M., Reshetnyak Yu. G., “O geometricheskikh svoistvakh funktsii s pervymi obobschennymi proizvodnymi”, Uspekhi mat. nauk, 34:1 (1979), 17–65 |
4. |
Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 |
5. |
Zorich V. A., “Sootvetstvie granits pri $Q$-kvazikonformnykh otobrazheniyakh shara”, Dokl. AN SSSR, 145:6 (1962), 1209–1212 |
6. |
Zorich V. A., “Granichnye svoistva odnogo klassa otobrazhenii v rostranstve”, Dokl. AN SSSR, 153:1 (1963), 23–26 |
7. |
Zorich V. A., “Opredelenie granichnykh elementov posredstvom sechenii”, Dokl. AN SSSR, 164:4 (1965), 736–739 |
8. |
Ignatev A. A., Ryazanov V. I., “Konechnoe srednee kolebanie v teorii otobrazhenii”, Ukr. mat. vestn., 2:3 (2005), 395–417 |
9. |
Kovtonyuk D. A., Petkov I. V., Ryazanov V. I., Salimov R. R., “Granichnoe povedenie i zadacha Dirikhle dlya uravnenii Beltrami”, Algebra i analiz, 25:4 (2013), 101–124 |
10. |
Kovtonyuk D. A., Ryazanov V. I., “K teorii granits prostranstvennykh oblastei”, Tr. IPMM NAN Ukrainy, 13, 2006, 110–120 |
11. |
Kovtonyuk D. A., Ryazanov V. I., “K teorii nizhnikh $Q$-gomeomorfizmov”, Ukr. mat. vestn., 5:2 (2008), 159–184 |
12. |
Kovtonyuk D. A., Ryazanov V. I., Salimov R. R., Sevostyanov E. A., “K teorii klassov Orlicha–Soboleva”, Algebra i analiz, 25:6 (2013), 50–102 |
13. |
Kovtonyuk D. A., Salimov R. R., Sevostyanov E. A., K teorii otobrazhenii klassov Soboleva i Orlicha–Soboleva, ed. Ryazanov V. I., Naukova dumka, Kiev, 2013 |
14. |
Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, Fizmatgiz, 1958 |
15. |
Lomako T. V., “O rasprostranenii nekotorykh obobschenii kvazikonformnykh otobrazhenii na granitsu”, Ukr. mat. zh., 61:10 (2009), 1329–1337 |
16. |
Mazya V. G., Prostranstva S. L. Soboleva, LGU, L., 1985 |
17. |
Reshetnyak Yu. G., Prostranstvennye otobrazheniya s ogranichennym iskazheniem, Nauka, Novosibirsk, 1982 |
18. |
Ryazanov V. I., Salimov R. R., “Slabo ploskie prostranstva i granitsy v teorii otobrazhenii”, Ukr. mat. vestn., 4:2 (2007), 199–234 |
19. |
Ryazanov V. I., Sevostyanov E. A., “Ravnostepenno nepreryvnye klassy koltsevykh $Q$-gomeomorfizmov”, Sib. mat. zh., 48:6 (2007), 1361–1376 |
20. |
Saks S., Teoriya integrala, IL, M., 1949 |
21. |
Sobolev S. L., Prilozheniya funktsionalnogo analiza v matematicheskoi fizike, LGU, L., 1950 |
22. |
Stepanoff W., “Sur les conditions de l'existence de la differentielle totale”, Mat. sb., 32:3 (1925), 511–527 |
23. |
Suvorov G. D., Obobschennyi printsip “dliny i ploschadi” v teorii otobrazhenii, Naukova dumka, Kiev, 1985 |
24. |
Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987 |
25. |
Shlyk V. A., “O ravenstve $p$-emkosti i $p$-modulya”, Sib. mat. zh., 34:6 (1993), 216–221 |
26. |
Adamowicz T., Björn A., Björn J., Shanmugalingam N., “Prime ends for domains in metric spaces”, Adv. Math., 238 (2013), 459–505 |
27. |
Birnbaum Z., Orlicz W., “Über die Verallgemeinerungen des Begriffes der zueinauder konjugierten Potenzen”, Studia Math., 3 (1931), 1–67 |
28. |
Calderon A. P., “On the differentiability of absolutely continuous functions”, Riv. Math. Univ. Parma, 2 (1951), 203–213 |
29. |
Caratheodory C., “Über die Begrenzung der einfachzusammenhängender Gebiete”, Math. Ann., 73:3 (1913), 323–370 |
30. |
Chiarenza F., Frasca M., Longo P., “$W^{2,p}$-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients”, Trans. Amer. Math. Soc., 336:2 (1993), 841–853 |
31. |
Collingwood E. F., Lohwator A. J., The theory of cluster sets, Cambridge Tracts in Math., 56, Cambridge Univ. Press, Cambridge, 1966 |
32. |
Freudenthal H., “Enden and Primenden”, Fund. Math., 39 (1952), 189–210 |
33. |
Gehring F. W., “Rings and quasiconformal mappings in space”, Trans. Amer. Math. Soc., 103:3 (1962), 353–393 |
34. |
Gehring F. W., Martio O., “Quasiextremal distance domains and extension of quasiconformal mappings”, J. Anal. Math., 45 (1985), 181–206 |
35. |
Gutlyanskii V., Ryazanov V., Srebro U., Yakubov E., The Beltrami equation. A geometric approach, Developments in Math., 26, Springer, New York, 2012 |
36. |
Heinonen J., Kilpelainen T., Martio O., Nonlinear potential theory of degenerate elliptic equations, Oxford Math. Monogr., Clarendon Press, New York, 1993 |
37. |
Hencl S., Koskela P., Lectures on mappings of finite distortion, Lecture Notes in Math., 2096, Springer, Cham, 2014 |
38. |
Iwaniec T., Martin G., Geometric function theory and non-linear analysis, Oxford Math. Monogr., Oxford Univ. Press, New York, 2001 |
39. |
Iwaniec T., Sbordone C., “Riesz transforms and elliptic PDEs with VMO coefficients”, J. Anal. Math., 74 (1998), 183–212 |
40. |
Iwaniec T., Sverák V., “On mappings with integrable dilatation”, Proc. Amer. Math. Soc., 118:1 (1993), 181–188 |
41. |
Kaufmann B., “Über die Berandung ebener und räumlicher Gebiete”, Math. Ann., 103:1 (1930), 70–144 |
42. |
Kovtonyuk D., Petkov I., Ryazanov V., Salimov R. R., “On the Dirichlet problem for the Beltrami equation”, J. Anal. Math., 122:4 (2014), 113–141 |
43. |
Kovtonyuk D., Petkov I., Ryazanov V., “On the boundary behaviour of solutions to the Beltrami equations”, Complex Var. Elliptic Equ., 58:5 (2013), 647–663 |
44. |
Kovtonyuk D., Ryazanov V., “On the theory of mappings with finite area distortion”, J. Anal. Math., 104 (2008), 291–306 |
45. |
Kovtonyuk D., Ryazanov V., “On the boundary behavior of generalized quasi-isometries”, J. Anal. Math., 115 (2011), 103–119 |
46. |
Kovtonyuk D. A., Ryazanov V. I., Salimov R. R., Sevost'yanov E. A., “On mappings in the Orlicz–Sobolev classes”, Ann. Univ. Buchar. Math. Ser., 3(LXI):1 (2012), 67–78 |
47. |
Lindelöf E., “Sur un principe general de l'analyse et ses applications á la theorie de la representation conforme”, Acta Soc. Sci. Fenn., 46:4 (1915), 1–35 |
48. |
Maly J., “A simple proof of the Stepanov theorem on differentiability almost everywhere”, Expo. Math., 17 (1999), 59–61 |
49. |
Martio O., Rickman S., Väisälä J., “Definitions for quasiregular mappings”, Ann. Acad. Sci. Fenn. Math., 448 (1969), 1–40 |
50. |
Martio O., Ryazanov V., Srebro U., Yakubov E., Moduli in modern mapping theory, Springer Monogr. Math., Springer, New York, 2009 |
51. |
Martio O., Ryazanov V., Vuorinen M., “BMO and injectivity of space quasiregular mappings”, Math. Nachr., 205 (1999), 149–161 |
52. |
Martio O., Vuorinen M., “Whitney cubes, $p$-capacity and Minkowski content”, Expo. Math., 5:1 (1987), 17–40 |
53. |
Mazurkiewicz S., “Über die Definition der Primenden”, Fund. Math., 26 (1936), 272–279 |
54. |
Mazurkiewicz S., “Recherches sur la theorie des bouts premiers”, Fund. Math., 33 (1945), 177–228 |
55. |
Näkki R., “Prime ends and quasiconformal mappings”, J. Anal. Math., 35 (1979), 13–40 |
56. |
Ohtsuka M., Extremal length and precise functions, Gakkotosho Co., Tokyo, 2003 |
57. |
Orlicz W., “Über eine gewisse Klasse von Räumen vom Typus B”, Bull. Intern. de l'Acad. Pol. Ser. A, 1932 (1932), 207–220, Cracovie |
58. |
Orlicz W., “Über Räume $(L^M)$”, Bull. Intern. de l'Acad. Pol. Ser. A, 1936 (1936), 93–107 |
59. |
Palagachev D. K., “Quasilinear elliptic equations with VMO coefficients”, Trans. Amer. Math. Soc., 347:7 (1995), 2481–2493 |
60. |
Rado T., Reichelderfer P. V., Continuous transformations in analysis, Grundlehren Math. Wiss., 75, Springer, Berlin, 1955 |
61. |
Ragusa M. A., “Elliptic boundary value problem in vanishing mean oscillation hypothesis”, Comment. Math. Univ. Carolin., 40:4 (1999), 651–663 |
62. |
Reimann H. M., Rychener T., Funktionen beschränkter mittlerer oscillation, Lecture Notes in Math., 487, Springer-Verlag, Berlin, 1975 |
63. |
Rickman S., Quasiregular mappings, Ergeb. Math. Grenzgeb. (3), 26, Springer-Verlag, Berlin, 1993 |
64. |
Ryazanov V., Salimov R., Srebro U., Yakubov E., “On boundary value problems for the Beltrami equations”, Contemp. Math., 591, Amer. Math. Soc., Providence, RI, 2013, 211–242 |
65. |
Ryazanov V., Sevost'yanov E., “Equicontinuity of mappings quasiconformal in the mean”, Ann. Acad. Sci. Fenn. Math., 36 (2011), 231–244 |
66. |
Ryazanov V., Srebro U., Yakubov E., “On ring solutions of Beltrami equation”, J. Anal. Math., 96 (2005), 117–150 |
67. |
Ryazanov V., Srebro U., Yakubov E., “To strong ring solutions of the Beltrami equations”, Uzbek. Math. J., 2009, no. 1, 127–137 |
68. |
Ryazanov V., Srebro U., Yakubov E., “On strong solutions of the Beltrami equations”, Complex Var. Elliptic Equ., 55:1–3 (2010), 219–236 |
69. |
Ryazanov V., Srebro U., Yakubov E., “Integral conditions in the theory of the Beltrami equations”, Complex Var. Elliptic Equ., 57:12 (2012), 1247–1270 |
70. |
Ryazanov V., Srebro U., Yakubov E., “Integral conditions in the mapping theory”, Ukr. mat. vestn., 7:1 (2010), 73–87 |
71. |
Sarason D., “Functions of vanishing mean oscillation”, Trans. Amer. Math. Soc., 207 (1975), 391–405 |
72. |
Ursell H. D., Young L. C., Remarks on the theory of prime ends, Mem. Amer. Mat. Soc., 1951, no. 3, 1951, 29 pp. |
73. |
Vasil'ev A., Moduli of families of curves for conformal and quasiconformal mappings, Lecture Notes in Math., 1788, Springer-Verlag, Berlin, 2002 |
74. |
Väisälä J., Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Math., 229, Springer-Verlag, Berlin, 1971 |
75. |
Vuorinen M., Conformal geometry and quasiregular mappings, Lecture Notes in Math., 1319, Springer-Verlag, Berlin, 1988 |
76. |
Whyburn G. Th., Analytic topology, Amer. Math. Soc. Collog. Publ., 28, Amer. Math. Soc., New York, 1942 |
77. |
Wilder R. L., Topology of manifolds, Amer. Math. Soc. Collog. Publ., 3, Amer. Math. Soc., New York, 1949 |
78. |
Zaanen A. C., Linear analysis. Measure and integral, Banach and Hilbert space, linear integral equations, Noordhoff N. V., Groningen, 1953 |
79. |
Ziemer W. P., “Extremal length and conformal capacity”, Trans. Amer. Math. Soc., 126:3 (1967), 460–473 |