Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2004_16_2_a2, author = {N. N. Romanovskii}, title = {Integral representations and embedding theorems for functions on the {Hesenberg} groups~$\mathbb H^n$}, journal = {Algebra i analiz}, pages = {82--119}, publisher = {mathdoc}, volume = {16}, number = {2}, year = {2004}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2004_16_2_a2/} }
TY - JOUR AU - N. N. Romanovskii TI - Integral representations and embedding theorems for functions on the Hesenberg groups~$\mathbb H^n$ JO - Algebra i analiz PY - 2004 SP - 82 EP - 119 VL - 16 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2004_16_2_a2/ LA - ru ID - AA_2004_16_2_a2 ER -
N. N. Romanovskii. Integral representations and embedding theorems for functions on the Hesenberg groups~$\mathbb H^n$. Algebra i analiz, Tome 16 (2004) no. 2, pp. 82-119. http://geodesic.mathdoc.fr/item/AA_2004_16_2_a2/
[1] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR
[2] Nečas J., Les méthodes directes en théorie des équations elliptiques, Masson, Paris, Academia, Prague, 1967
[3] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, 1-oe izd., Nauka, M., 1969 ; 2-ое изд., 1977 | MR
[4] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR
[5] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl
[6] Goldshtein V. M., Reshetnyak Yu. G., Vvedenie v teoriyu funktsii s obobschennymi proizvodnymi i kvazikonformnye otobrazheniya, Nauka, M., 1983 | MR
[7] Mazya V. G., Prostranstva S. L. Soboleva, LGU, L., 1985 | MR
[8] Adams D. R., Hedberg L. I., Function spaces and potential theory, Grundlehren Math. Wiss., 314, Springer-Verlag, Berlin, 1996 | MR
[9] Burenkov V. I., Sobolev spaces on domains, Teubner-Texte Math., 137, Teubner, Stuttgart, 1998 | MR | Zbl
[10] Reshetnyak Yu. G., Teoremy ustoichivosti v geometrii i analize, In-t matematiki SO RAN, Novosibirsk, 1996 | MR
[11] Aronszajn N., Mulla F., Szeptycki P., “On spaces of potentials connected with $L_p$ classes”, Ann. Inst. Fourier (Grenoble), 13 (1963), 211–306 | MR | Zbl
[12] Besov O. V., Ilin V. P., “Estestvennoe rasshirenie klassa oblastei v teoremakh vlozheniya”, Mat. sb., 75(117):4 (1968), 483–495 | MR | Zbl
[13] Smith K. T., “Formulas to represent functions by their derivatives”, Math. Ann., 188 (1970), 53–77 | DOI | MR
[14] Reshetnyak Yu. G., “Nekotorye integralnye predstavleniya differentsiruemykh funktsii”, Sib. mat. zh., 12:2 (1971), 420–432
[15] Uspenskii S. V., “O predstavlenii funktsii, opredelyaemykh odnim klassom gipoellipticheskikh operatorov”, Tr. Mat. in-ta AN SSSR, 117, 1972, 292–299 | MR | Zbl
[16] Burenkov V. I., “Integralnoe predstavlenie Soboleva i formula Teilora”, Tr. Mat. in-ta AN SSSR, 131, 1974, 33–38 | MR | Zbl
[17] Perepelkin V. G., “Integralnye predstavleniya funktsii, prinadlezhaschikh vesovym klassam S. L. Soboleva v oblastyakh, i nekotorye prilozheniya. I, II”, Sib. mat. zh., 17 (1976), 119–140 ; 318–330 | MR | Zbl | Zbl
[18] Goodman R. W., Nilpotent Lie groups: structure and applications to analysis, Lecture Notes in Math., 562, Springer-Verlag, Berlin–New York, 1976 | MR | Zbl
[19] Coifman R., Weiss G., Analyse harmonique non-commutative sur certains espaces homogenes. Étude de Certaines Intégrates Singulières, Lecture Notes in Math., 242, Springer-Verlag, Berlin–New York, 1971 | MR | Zbl
[20] Folland G. B., “Subelliptic estimates and function spaces on nilpotent Lie groups”, Ark. Mat., 13:2 (1975), 161–207 | DOI | MR | Zbl
[21] Folland G. B., Stein E. M., Hardy spaces on homogeneous groups, Math. Notes, 28, Princeton Univ. Press, Princeton, NJ, 1982 | MR | Zbl
[22] Korányi A., Vági S., “Singular integrals on homogeneous spaces and some problems of classical analysis”, Ann. Scuola Norm. Sup. Pisa (3), 25 (1971) (1972), 575–648 | MR | Zbl
[23] Korányi A., Reimann H. M., “Foundations for the theory of quasiconformal mappings on the Heisenberg group”, Adv. Math., 111:1 (1995), 1–87 | DOI | MR | Zbl
[24] Rothschild L. P., Stein E. M., “Hypoelliptic differential operators and nilpotent groups”, Acta Math., 137 (1976), 247–320 | DOI | MR
[25] Gromov M., Carnot-Carathéodory spaces seen from within, Preprint no. IHES/M/94/6, Inst. Hautes Études Sci., Bures-sur-Yvette, 1994
[26] Gromov M., Pansu P., “Rigidity of lattices: an introduction”, Geometric Topology: Recent Development (Montecatini Terme, 1990), Lecture Notes in Math., 1504, Springer, Berlin, 1991, 39–137 | MR
[27] Nagel A., Stein E. M., Wainger S., “Balls and metrics defined by vector fields. I. Basic properties”, Acta Math., 155 (1985), 103–147 | DOI | MR | Zbl
[28] Pansu P., “Métriques de Carnot–Carathéodory et quasiisométries des espaces symétriques de rang un”, Ann. of Math. (2), 129 (1989), 1–60 | DOI | MR | Zbl
[29] Jerison D., “The Poincaré inequality for vector fields satisfying Hörmander's condition”, Duke Math. J., 53:2 (1986), 503–523 | DOI | MR | Zbl
[30] Jerison D., Lee J. M., “Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem”, J. Amer. Math. Soc., 1:1 (1988), 1–13 | DOI | MR | Zbl
[31] Jerison D., Sánchez-Calle A., “Subelliptic, second order differential operators”, Complex Analysis, III (College Park, Md., 1985–86), Lecture Notes in Math., 1277, Springer, Berlin, 1987, 46–77 | MR
[32] Franchi B., “Weighted Sobolev–Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations”, Trans. Amer. Math. Soc., 327 (1991), 125–158 | DOI | MR | Zbl
[33] Franchi B., Gutiérrez C. E., Wheeden R. L., “Weighted Sobolev–Poincare inequalities for Grushin type operators”, Comm. Partial Differential Equations, 19 (1994), 523–604 | DOI | MR | Zbl
[34] Franchi B., Lanconelli E., “Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 10:4 (1983), 523–541 | MR | Zbl
[35] Franchi B., Lanconelli E., “An embedding theorem for Sobolev spaces related to nonsmooth vector fields and Harnack inequality”, Comm. Partial Differential Equations, 9 (1984), 1237–1264 | DOI | MR | Zbl
[36] Franchi B., Lu G., Wheeden R. L., “Representation formulas and weighted Poincaré inequalities for Hörmander vector fields”, Ann. Inst. Fourier (Grenoble), 45:2 (1995), 577–604 | MR | Zbl
[37] Franchi B., Lu G., Wheeden R. L., “A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type”, Internat. Math. Res. Notices, 1996:1 (1996), 1–14 | DOI | MR | Zbl
[38] Capogna L., Garofalo N., “Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot–Carathéodory metrics”, J. Fourier Anal. Appl., 4:4–5 (1998), 403–432 | DOI | MR | Zbl
[39] Danielli D., “Formules de représentation et théorèmes d'inclusion pour des opérateurs sous-elliptiques”, C. R. Acad. Sci. Paris Sér. 1 Math., 314:13 (1992), 987–990 | MR | Zbl
[40] Danielli D., Garofalo N., Nhieu D.-M., “Trace inequalities for Carnot–Carathéodory spaces and applications”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 27 (1998):2 (1999), 195–252 | MR
[41] Garofalo N., Lanconelli E., “Existence and nonexistence results for semilinear equations on the Heisenberg group”, Indiana Univ. Math. J., 41:1 (1992), 71–98 | DOI | MR | Zbl
[42] Garofalo N., Nhieu D.-M., A general extension theorem for Sobolev spaces arising from system of non-commuting vector fields, Preprint, 1996 | MR
[43] Hajlazs P., Koskela P., Sobolev met Poincaré, Mem. Amer. Math. Soc., 145, no. 688, 2000 | MR
[44] Hajlasz P., Martio O., “Traces of Sobolev functions on fractal type sets and characterization of extension domains”, J. Fund. Anal., 143 (1997), 221–246 | DOI | MR | Zbl
[45] Heinonen J., Koskela P., “Weighted Sobolev and Poincaré inequalities and quasiregular mappings of polynomial type”, Math. Scand., 77 (1995), 251–271 | MR | Zbl
[46] Lu G., “Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications”, Rev. Mat. Iberoamericana, 8:3 (1992), 367–439 | MR | Zbl
[47] Lu G., “Existence and size estimates for the Green's functions of differential operators constructed from degenerate vector fields”, Comm. Partial Differential Equations, 17 (1992), 1213–1251 | MR | Zbl
[48] Lu G., “Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations”, Publ. Mat., 40 (1996), 301–329 | MR | Zbl
[49] Lu G., “A note on a Poincaré type inequality for solutions to subelliptic equations”, Comm. Partial Differential Equations, 21 (1996), 235–254 | DOI | MR
[50] Vodopyanov S. K., “$L_p$-teoriya potentsiala i kvazikonformnye otobrazheniya na odnorodnykh gruppakh”, Sovremennye problemy geometrii i analiza, Tr. In-ta mat. SO AN SSSR, 14, Nauka, SO, Novosibirsk, 1989, 45–89 | MR
[51] Vodopyanov S. K., “Vesovaya $L_p$-teoriya potentsiala na odnorodnykh gruppakh”, Sib. mat. zh., 33:2 (1992), 29–48 | MR
[52] Vodopyanov S. K., “Kvazikonformnye otobrazheniya na gruppakh Karno i ikh primeneniya”, Dokl. RAN, 347:4 (1996), 439–442 | MR
[53] Vodopyanov S. K., “Monotonnye funktsii i kvazikonformnye otobrazheniya na gruppakh Karno”, Sib. mat. zh., 37:6 (1996), 1269–1295 | MR
[54] Vodopyanov S. K., Greshnov A. V., “O prodolzhenii funktsii ogranichennoi srednei ostsillyatsii na prostranstvakh odnorodnogo tipa s vnutrennei metrikoi”, Sib. mat. zh., 36:5 (1995), 1015–1048 | MR
[55] Vodopyanov S. K., Greshnov A. V., “Analiticheskie svoistva kvazikonformnykh otobrazhenii na gruppakh Karno”, Sib. mat. zh., 36:6 (1995), 1317–1327 | MR
[56] Vodopyanov S. K., Greshnov A. V., “Prodolzhenie differentsiruemykh funktsii i kvazikonformnye otobrazheniya na gruppakh Karno”, Dokl. RAN, 348:1 (1996), 15–18 | MR
[57] Vodopyanov S. K., Chernikov V. M., “Prostranstva Soboleva i gipoellipticheskie uravneniya”, Lineinye operatory, soglasovannye s poryadkom, Tr. In-ta mat. SO RAN, 29, In-t mat. SO RAN, Novosibirsk, 1995, 7–62 | MR
[58] Vodop'yanov S. K., “$\mathcal P$-differentiability on Carnot groups in different topologies and related topics”, Trudy po analizu i geometrii, In-t mat. SO RAN, Novosibirsk, 2000, 603–670 | MR
[59] Greshnov A. V., “Prodolzhenie differentsiruemykh funktsii za granitsu oblasti na gruppakh Karno”, Tr. In-ta mat. SO RAN, 31, In-t mat. SO RAN, Novosibirsk, 1996, 161–186 | MR | Zbl
[60] Korn A., “Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen”, Krak. Anz., 1909, 705–724 | Zbl
[61] Aronszajn N., “On coercive integro-differential quadratic forms”, Report no. 14, Univ. Kansas, 1954, 94–106
[62] Smith K. T., “Inequalities for formally positive integro-differential forms”, Bull. Amer. Math. Soc., 67 (1961), 368–370 | DOI | MR | Zbl
[63] Besov O. V., “O koertsitivnosti v neizotropnom prostranstve S. L. Soboleva”, Mat. sb., 73(115):4 (1967), 585–599 | MR | Zbl
[64] Agmon S., Duglis A., Nirenberg L., Otsenki vblizi granitsy reshenii ellipticheskikh uravnenii v chastnykh proizvodnykh pri obschikh granichnykh usloviyakh, IL, M., 1962
[65] Kondratev V. A., Oleinik O. A., “Kraevye zadachi dlya sistemy teorii uprugosti v neogranichennykh oblastyakh. Neravenstva Korna”, Uspekhi mat. nauk, 43:5 (1988), 55–98 | MR
[66] Fikera G., Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974
[67] Glushko V. P., “Ob oblastyakh, zvezdnykh otnositelno shara”, Dokl. AN SSSR, 144:6 (1962), 1215–1216 | Zbl
[68] Romanovskii N. N., “Koertsitivnye otsenki dlya lineinykh differentsialnykh operatorov s postoyannymi koeffitsientami”, Mat. zametki, 70:2 (2001), 316–320 | MR | Zbl
[69] Romanovskii N. N., “Integralnye predstavleniya i teoremy vlozheniya dlya funktsii, zadannykh na gruppakh Geizenberga $\mathbb H^n$”, Dokl. RAN, 382:4 (2002), 456–459 | MR | Zbl
[70] Romanovskii N. N., “Neravenstva tipa Korna na gruppakh Geizenberga i zadacha Neimana dlya lineinykh subellipticheskikh sistem”, Dokl. RAN, 383:1 (2002), 24–27 | MR | Zbl