Geodesic
Potential theory on homogeneous groups
Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 59-81 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This article is concerned with potential theory on homogeneous groups, and is of theoretical significance. Bibliography: 28 titles. 
@article{SM_1990_66_1_a2,
     author = {S. K. Vodop'yanov},
     title = {Potential theory on homogeneous groups},
     journal = {Sbornik. Mathematics},
     pages = {59--81},
     year = {1990},
     volume = {66},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_66_1_a2/}
}
TY  - JOUR
AU  - S. K. Vodop'yanov
TI  - Potential theory on homogeneous groups
JO  - Sbornik. Mathematics
PY  - 1990
SP  - 59
EP  - 81
VL  - 66
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1990_66_1_a2/
LA  - en
ID  - SM_1990_66_1_a2
ER  - 
%0 Journal Article
%A S. K. Vodop'yanov
%T Potential theory on homogeneous groups
%J Sbornik. Mathematics
%D 1990
%P 59-81
%V 66
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1990_66_1_a2/
%G en
%F SM_1990_66_1_a2
S. K. Vodop'yanov. Potential theory on homogeneous groups. Sbornik. Mathematics, Tome 66 (1990) no. 1, pp. 59-81. http://geodesic.mathdoc.fr/item/SM_1990_66_1_a2/

[1] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[2] Karleson L., Izbrannye problemy teorii isklyuchitelnykh mnozhestv, Mir, M., 1971 | MR | Zbl

[3] Reshetnyak Yu. T., “O ponyatii emkosti v teorii funktsii s obobschennymi proizvodnymi”, Sib. matem. zhurn., 10:5 (1969), 1109–1138 | MR | Zbl

[4] Mazya V. G., Khavin V. P., “Nelineinaya teoriya potentsiala”, UMN, 27:6 (1972), 67–138 | MR | Zbl

[5] Adams D. R., Meyers N. G., “Bessel potentials. Inclusion relations among classes of exceptional sets”, Indiana Univ. Math. J., 22:9 (1973), 873–905 | DOI | MR | Zbl

[6] Hedberg L. I., Wolff T. H., “Thin sets in nonlinear potential theory”, Ann. Inst. Fourier (Grenoble), 33:4 (1983), 161–187 | MR | Zbl

[7] Vodopyanov S. K., “Kvaziellipticheskaya $L_p$-teoriya potentsiala i ee prilozheniya”, DAN SSSR, 298:4 (1988), 780–784 | MR | Zbl

[8] Vodopyanov S. K., “Sravnenie metricheskikh i emkostnykh kharakteristik v teorii potentsiala”, Tez. dokl. Vsesoyuzn. shkoly po kompleksnomu analizu i matematicheskoi fizike (Divnogorsk, iyun–iyul 1987 g.), Krasnoyarsk, 1987, 20

[9] Vodopyanov S. K, “Printsip maksimuma v teorii potentsiala i teoremy vlozheniya dlya anizotropnykh prostranstv differentsiruemykh funktsii”, Sib. matem. zhurn., 29:2 (1988), 17–33 | MR

[10] Vodopyanov S. K., “Geometricheskie svoistva otobrazhenii i oblastei. Otsenki snizu normy operatora prodolzheniya”, Issledovaniya po geometrii i matematicheskomu analizu, Tr. In-ta matematiki, 7, ed. Yu. G. Reshetnyak, Nauka, Novosibirsk, 1987, 70–101 | MR

[11] Vodopyanov S. K., “Izoperimetricheskie sootnosheniya i usloviya prodolzheniya differentsiruemykh funktsii”, DAN SSSR, 292:1 (1987), 11–15 | MR

[12] Vodopyanov S. K., “Geometricheskie svoistva oblastei i otsenki dlya normy operatora prodolzheniya”, DAN SSSR, 292:4 (1987), 791–795 | MR

[13] Alborova M. S, Vodopyanov S. K., Ustranimye osobennosti reshenii kvaziellipticheskikh uravnenii, Novosib. gos. un-t., Novosibirsk, 1987, 44 pp., Dep. v VINITI 04.02.87, No 804-V87 | MR

[14] Folland G. B., Stein E. M., Hardy spaces on homogeneous groups, Math. Notes, 28, Princ. Univ. Press, 1982 | MR | Zbl

[15] Fabes E. B., Riveire N. M., “Singular integrals with Homogeneity”, Studia Math, 27 (1966), 19–38. | MR | Zbl

[16] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[17] Stein E. M., Wainger S., “Problems in harmonic analysis related with curvature”, Bull. Amer. Math. Soc., 84 (1978), 1239–1295 | DOI | MR | Zbl

[18] Adams D. R., “Weighted nonlinear potential theory”, Trans. Amer. Math. Soc., 297:1 (1986), 73–94 | DOI | MR | Zbl

[19] Muckenhoupt B., Wheeden R. L., “Weighted norm Inequalities for fractional Integrals”, Trans. Amer. Math. Soc., 192:6 (1974), 261–274 | DOI | MR | Zbl

[20] Goldshtein V. M., Reshetnyak Yu. G., Vvedenie v teoriyu funktsii s obobschennymi proizvodnymi i kvazikonformnye otobrazheniya, Nauka, M., 1983 | MR

[21] Meyers N. G., “A theory of capacities for potentials of functions in Lebesque classes”, Math. Scand., 26:2 (1970), 255–292 | MR | Zbl

[22] Lizorkin P. I., “Obobschennoe liuvillevskoe differentsirovanie i metod multiplikatorov v teorii vlozhenii klassov differentsiruemykh funktsii”, Tr. MIAN, 105 (1969), 89–167 | MR | Zbl

[23] Dappa H., Trebels W., “On $L^1$-criteria for quasiradial Fourier multipliers with applications to some anisotropic function spaces”, Anal. Math., 9:4 (1983), 275–289 | DOI | MR | Zbl

[24] Wiener N., “The Dirichlet problem”, J. Math. Phys. Mass. Inst. Tech., 3 (1924), 127–146 | Zbl

[25] Mazya V. G., “O nepreryvnosti v granichnoi tochke reshenii kvazilineinykh ellipticheskikh uravnenii”, Vestn. LGU. Matematika. Mekhanika. Astronomiya, 27:13 (1970), 42–55; 27:1 (1972), 160

[26] Gariepy R., Ziemer W. P., “A regularity condition at the boundary for solutions of quasilinear elliptic equations”, Arch. Rat. Mech. Anal., 67:1 (1977), 25–39 | DOI | MR | Zbl

[27] Skrypnik I. V., “Kriterii regulyarnosti granichnoi tochki dlya kvazilineinykh ellipticheskikh uravnenii”, DAN SSSR, 274:6 (1984), 1040–1043 | MR

[28] Lindqvist P., Martio O., “Two theorems of N. Wiener for solutions of quasilinear elliptic equations”, Acta Math., 155 (1988), 153–171 | DOI | MR