Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2017_14_a121, author = {A. S. Romanov}, title = {The composition operators in {Sobolev} spaces with variable exponent of summability}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {794--806}, publisher = {mathdoc}, volume = {14}, year = {2017}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a121/} }
TY - JOUR AU - A. S. Romanov TI - The composition operators in Sobolev spaces with variable exponent of summability JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2017 SP - 794 EP - 806 VL - 14 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a121/ LA - ru ID - SEMR_2017_14_a121 ER -
A. S. Romanov. The composition operators in Sobolev spaces with variable exponent of summability. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 794-806. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a121/
[1] S.L. Sobolev, “On some transformation groups of an $n$-dimensional space”, Dokl. Akad. Nauk SSSR, 32:6 (1941), 380–382 | Zbl
[2] S.K. Vodop'yanov, V.M. Gol'dshtein, “Lattice isomorphisms of the spaces $W_n^1$ and quasiconformal mappings”, Siberian Math. J., 16:2 (1975), 224–246 | MR | Zbl
[3] S.K. Vodop'yanov, V.M. Gol'dshtein, “Functional characteristics of quasiisometric mappings”, Siberian Math. J., 17:4 (1976), 768–773 | MR | Zbl
[4] S.K. Vodop'yanov, V.M. Gol'dshtein, “A new function-theoretic invariant for quasiconformal mappings”, Proceedings of the conference «Some problems of modern theory of functions», Inst. Mat., Novosibirsk, 1976, 18–20
[5] S.K. Vodop'yanov, “$L_p$-potential theory and quasiconformal mappings on homogeneous groups”, Contemporary problems of geometry and analysis, Nauka, Novosibirsk, 1989, 45–89 | Zbl
[6] A.S. Romanov, “Change of variable in spaces of Bessel and Riesz potentials”, Functional analysis and mathematical physics, 135, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1985, 117–133 (Russian) | MR
[7] S.K. Vodop'yanov, N.A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings”, Siberian Math. J., 56:5 (2015), 989–1029 | MR | Zbl
[8] S.K. Vodopyanov, “Composition Operators on Sobolev Spaces”, Complex Analysis and Dynamical Systems II, A Conference in Honor of Professor Lawrence Zalcman's Sixtieth Birthday (June 9–12, 2003, Nahariya, Israel), AMS Contemporary Mathematics, 382, eds. M. Agranovsky, L. Karp, D. Shoikhet, Ann Arbor, 2005, 327–342 | MR
[9] O. Kovacik, J. Rakosnik, “On spaces $L^{p(x)}$ and $W^{k,p(x)}$”, Czechoslovak Math. J., 41:4 (1991), 592–618 | MR | Zbl
[10] P. Harjulehto, P. Hästö, M. Pere, “Variable Exponent Lebesgue Spaces on Metric Spaces: The Hardy–Littlewood Maximal Operator”, Real Analysis Exchange, 30:1 (2004/2005), 87–104 | DOI | MR
[11] T. Adamowicz, P. Harjulehto, P. Hästö, Maximal operator in varible exponent Lebesgue spaces on unbounded quasimetric measure spaces, , 1–13 pp. (Received by the editors 14.12.2012) http://www.helsinki.fi/p̃harjule/varsob/pdf/maximal-submitted.pdf
[12] A.S. Romanov, “Sobolev-type functions with variable integrability exponent on metric measure spaces”, Siberian Math. J., 55:1 (2014), 178–194 | DOI | MR | Zbl
[13] L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions, Textbooks in Mathematics, CRC Press, Boca Raton, FL, 2015 | MR | Zbl
[14] V.M. Gol'dshtein, Yu.G. Reshetnyak, Quasiconformal mappings and Sobolev spaces, Translated and revised from the 1983 Russian original, translated by O. Korneeva, Mathematics and its Applications (Soviet Series), 54, Kluwer Academic Publishers Group, Dordrecht, 1990 | MR | Zbl