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Volumn 52, Issue 2, 2008, Pages 347-363

Sobolev inequalities with variable exponent attaining the values 1 and n

Author keywords

Limit case; Sobolev inequality; Sobolev space; Variable exponent

Indexed keywords


EID: 52649129724     PISSN: 02141493     EISSN: None     Source Type: Journal    
DOI: 10.5565/PUBLMAT_52208_05     Document Type: Article
Times cited : (55)

References (28)
  • 1
    • 34547186223 scopus 로고    scopus 로고
    • Characterization of Riesz and Bessel potentials on variable Lebesgue spaces
    • A. ALMEIDA AND S. SAMKO, Characterization of Riesz and Bessel potentials on variable Lebesgue spaces, J. Funct. Spaces Appl. 4(2) (2006), 113-144.
    • (2006) J. Funct. Spaces Appl , vol.4 , Issue.2 , pp. 113-144
    • ALMEIDA, A.1    SAMKO, S.2
  • 2
    • 34547194180 scopus 로고    scopus 로고
    • Pointwise inequalities in variable Sobolev spaces and applications
    • A. ALMEIDA AND S. SAMKO, Pointwise inequalities in variable Sobolev spaces and applications, Z. Anal. Anwend. 26(2) (2007), 179-193.
    • (2007) Z. Anal. Anwend , vol.26 , Issue.2 , pp. 179-193
    • ALMEIDA, A.1    SAMKO, S.2
  • 3
    • 52649122628 scopus 로고    scopus 로고
    • B. BOJARSKI, Remarks on Sobolev imbedding inequalities, in: Complex analysis (Joensuu 1987), Lecture Notes in Math. 1351, Springer, Berlin, 1988, pp. 52-68.
    • B. BOJARSKI, Remarks on Sobolev imbedding inequalities, in: "Complex analysis" (Joensuu 1987), Lecture Notes in Math. 1351, Springer, Berlin, 1988, pp. 52-68.
  • 4
    • 52649098359 scopus 로고    scopus 로고
    • On the Sobolev-type inequality for Lebesgue spaces with a variable exponent
    • B. CEKIC, R. MASHIYEV, AND G. T. ALISOY, On the Sobolev-type inequality for Lebesgue spaces with a variable exponent, Int. Math. Forum 1 (2006), no. 25-28, 1313-1323.
    • (2006) Int. Math. Forum , vol.1 , Issue.25-28 , pp. 1313-1323
    • CEKIC, B.1    MASHIYEV, R.2    ALISOY, G.T.3
  • 7
    • 2642523897 scopus 로고    scopus 로고
    • Maximal function on generalized Lebesgue spaces Lp(.)
    • p(.) Math. Inequal. Appl. 7(2) (2004), 245-253.
    • (2004) Math. Inequal. Appl , vol.7 , Issue.2 , pp. 245-253
    • DIENING, L.1
  • 8
    • 4544323976 scopus 로고    scopus 로고
    • p(.) and W k,p(.)
    • k,p(.) Math. Nachr. 268 (2004), 31-43.
    • (2004) Math. Nachr , vol.268 , pp. 31-43
    • DIENING, L.1
  • 9
    • 52649145206 scopus 로고    scopus 로고
    • Maximal functions in variable exponent spaces: Limiting cases of the exponent
    • Preprint
    • L. DIENING, P. HARJULEHTO, P. HÄSTÖ, Y. MIZUTA, AND T. SHIMOMURA, Maximal functions in variable exponent spaces: limiting cases of the exponent, Preprint (2007).
    • (2007)
    • DIENING, L.1    HARJULEHTO, P.2    HÄSTÖ, P.3    MIZUTA, Y.4    SHIMOMURA, T.5
  • 10
    • 52649124706 scopus 로고    scopus 로고
    • L. DIENING, P. HÄSTÖ, AND A. NEKVINDA, Open problems in variable exponent Lebesgue and Sobolev spaces, in: FSDONA04 Proceedings (Drabek and Rákosník (eds.); Milovy, Czech Republic, 2004), Academy of Sciences of the Czech Republic, Prague, 2005, pp. 38-58.
    • L. DIENING, P. HÄSTÖ, AND A. NEKVINDA, Open problems in variable exponent Lebesgue and Sobolev spaces, in: "FSDONA04 Proceedings" (Drabek and Rákosník (eds.); Milovy, Czech Republic, 2004), Academy of Sciences of the Czech Republic, Prague, 2005, pp. 38-58.
  • 11
    • 0001385278 scopus 로고    scopus 로고
    • Sobolev embeddings with variable exponent
    • D. E. EDMUNDS AND J. RÁKOSNÍK, Sobolev embeddings with variable exponent, Studia Math. 143(3) (2000), 267-293.
    • (2000) Studia Math , vol.143 , Issue.3 , pp. 267-293
    • EDMUNDS, D.E.1    RÁKOSNÍK, J.2
  • 12
    • 18744420357 scopus 로고    scopus 로고
    • Sobolev embeddings with variable exponent. II
    • D. E. EDMUNDS AND J. RÁKOSNÍK, Sobolev embeddings with variable exponent. II, Math. Nachr. 246/247 (2002), 53-67.
    • (2002) Math. Nachr , vol.246-247 , pp. 53-67
    • EDMUNDS, D.E.1    RÁKOSNÍK, J.2
  • 13
    • 33846554976 scopus 로고    scopus 로고
    • Sobolev embeddings for variable exponent Riesz potentials on metric spaces
    • T. FUTAMURA, Y. MIZUTA, AND T. SHIMOMURA, Sobolev embeddings for variable exponent Riesz potentials on metric spaces, Ann. Acad. Sci. Fenn. Math. 31(2) (2006), 495-522.
    • (2006) Ann. Acad. Sci. Fenn. Math , vol.31 , Issue.2 , pp. 495-522
    • FUTAMURA, T.1    MIZUTA, Y.2    SHIMOMURA, T.3
  • 15
    • 27644465907 scopus 로고    scopus 로고
    • A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces
    • P. HARJULEHTO AND P. HÄSTÖ, A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces, Rev. Mat. Complut. 17(1) (2004), 129-146.
    • (2004) Rev. Mat. Complut , vol.17 , Issue.1 , pp. 129-146
    • HARJULEHTO, P.1    HÄSTÖ, P.2
  • 16
    • 33748530360 scopus 로고    scopus 로고
    • Sobolev embeddings in metric measure spaces with variable dimension
    • P. HARJULEHTO, P. HÄSTÖ, AND V. LATVALA, Sobolev embeddings in metric measure spaces with variable dimension, Math. Z. 254(3) (2006), 591-609.
    • (2006) Math. Z , vol.254 , Issue.3 , pp. 591-609
    • HARJULEHTO, P.1    HÄSTÖ, P.2    LATVALA, V.3
  • 17
    • 38649116003 scopus 로고    scopus 로고
    • Minimizers of the variable exponent, non-uniformly convex Dirichlet energy
    • P. HARJULEHTO, P. HÄSTÖ, AND V. LATVALA, Minimizers of the variable exponent, non-uniformly convex Dirichlet energy, J. Math. Pures Appl. (9) 89(2) (2008), 174-197.
    • (2008) J. Math. Pures Appl. (9) , vol.89 , Issue.2 , pp. 174-197
    • HARJULEHTO, P.1    HÄSTÖ, P.2    LATVALA, V.3
  • 18
    • 85035060141 scopus 로고    scopus 로고
    • Variable exponent Lebesgue spaces on metric spaces: The Hardy-Littlewood maximal operator
    • P. HARJULEHTO, P. HÄSTÖ, AND M. PERE, Variable exponent Lebesgue spaces on metric spaces: the Hardy-Littlewood maximal operator, Real Anal. Exchange 30(1) (2004/05), 87-103.
    • (2005) Real Anal. Exchange , vol.30 , Issue.1 , pp. 87-103
    • HARJULEHTO, P.1    HÄSTÖ, P.2    PERE, M.3
  • 19
    • 84968517735 scopus 로고
    • On certain convolution inequalities
    • L. I. HEDBERG, On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505-510.
    • (1972) Proc. Amer. Math. Soc , vol.36 , pp. 505-510
    • HEDBERG, L.I.1
  • 20
    • 1342283933 scopus 로고    scopus 로고
    • On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent
    • V. KOKILASHVILI AND S. SAMKO, On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent, Z. Anal. Anwendungen 22(4) (2003), 899-910.
    • (2003) Z. Anal. Anwendungen , vol.22 , Issue.4 , pp. 899-910
    • KOKILASHVILI, V.1    SAMKO, S.2
  • 21
    • 52649155861 scopus 로고    scopus 로고
    • k,p(x), Czechoslovak Math. J. 41(116) (1991), no. 4, 592-618.
    • k,p(x), Czechoslovak Math. J. 41(116) (1991), no. 4, 592-618.
  • 22
    • 0001552241 scopus 로고
    • John domains, bi-Lipschitz balls and Poincaré inequality
    • O. MARTIO, John domains, bi-Lipschitz balls and Poincaré inequality, Rev. Roumaine Math. Pures Appl. 33(1-2) (1988), 107-112.
    • (1988) Rev. Roumaine Math. Pures Appl , vol.33 , Issue.1-2 , pp. 107-112
    • MARTIO, O.1
  • 24
    • 24744459050 scopus 로고    scopus 로고
    • Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity
    • Y. MIZUTA AND T. SHIMOMURA, Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity, J. Math. Anal. Appl. 311(1) (2005), 268-288.
    • (2005) J. Math. Anal. Appl , vol.311 , Issue.1 , pp. 268-288
    • MIZUTA, Y.1    SHIMOMURA, T.2
  • 25
    • 0003311060 scopus 로고
    • Orlicz spaces and modular spaces
    • Springer-Verlag, Berlin
    • J. MUSIELAK, "Orlicz spaces and modular spaces", Lecture Notes in Mathematics 1034, Springer-Verlag, Berlin, 1983.
    • (1983) Lecture Notes in Mathematics , vol.1034
    • MUSIELAK, J.1
  • 26
    • 0037932530 scopus 로고    scopus 로고
    • p(x) on which the Hardy-Littlewood maximal operator is not bounded
    • p(x) on which the Hardy-Littlewood maximal operator is not bounded, Expo. Math. 19(4) (2001), 369-371.
    • (2001) Expo. Math , vol.19 , Issue.4 , pp. 369-371
    • PICK, L.1    RŮŽICKA, M.2
  • 27
    • 27844475999 scopus 로고    scopus 로고
    • On a progress in the theory of Lebesgue spaces with variable exponent: Maximal and singular operators
    • S. SAMKO, On a progress in the theory of Lebesgue spaces with variable exponent: maximal and singular operators, Integral Transforms Spec. Funct. 16(5-6) (2005), 461-482.
    • (2005) Integral Transforms Spec. Funct , vol.16 , Issue.5-6 , pp. 461-482
    • SAMKO, S.1
  • 28
    • 33750326642 scopus 로고    scopus 로고
    • Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators. II
    • S. SAMKO, E. SHARGORODSKY, AND B. VAKULOV, Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators. II, J. Math. Anal. Appl. 325(1) (2007), 745-751.
    • (2007) J. Math. Anal. Appl , vol.325 , Issue.1 , pp. 745-751
    • SAMKO, S.1    SHARGORODSKY, E.2    VAKULOV, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.