Maximal function on generalized lebesgue spaces Lp(·)

Mathematical Inequalities and Applications

Volumn 7, Issue 2, 2004, Pages 245-253

  Diening, L ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Electrorheological fluids; Generalized Lebesgue spaces; Generalized Orlicz spaces; Maximal function; Mollifier

Indexed keywords

EID: 2642523897     PISSN: 13314343     EISSN: None     Source Type: Journal    
DOI: 10.7153/mia-07-27     Document Type: Article

References (19)

1. EMILIO ACERBI AND GIUSEPPE MINGIONE, Regularity results for a class of functionals with non-standard growth, Arch. Ration. Mech. Anal. 156 (2001), no. 2, 121-140.
2. JÖRAN BEROH AND JÖRGEN LÖFSTRÖM, Interpolation spaces. An introduction. Springer-Verlag, Berlin, 1976, Grundlehren der Mathematischen Wissenschaften, No. 223.
3. LARS DIENING, Theoretical and numerical results for electrorheological fluids, Ph.D. thesis, University of Freiburg, Germany, 2002.
4. k,p(x) (Ω), Proc. Roy. Soc. London Ser. A 437 (1992), no. 1899, 229-236.
5. _, Sobolev embeddings with variable exponent, Studia Math. 143 (2000), no. 3, 267-293.
6. LAWRENCE C. EVANS AND RONALD F. GARIEPY, Measure theory and fine properties of functions, CRC Press, Boca Raton, FL, 1992.
7. k(Ω), Comment. Math. Prace Mat. 21 (1980), no. 2, 315-324.
8. k,p(x), Czechoslovak Math. J. 41(116) (1991), no. 4, 592-618.
9. PAOLO MARCELLINI, Regularity and existence of solutions of elliptic equations with p, q -growth conditions, J. Differential Equations 90 (1991), no. 1, 1-30.
10. J. MUSIEŁAK AND W. ORLICZ, On modular spaces, Studia Math. 18 (1959), 49-65.
11. JULIAN MUSIELAK, Orlicz spaces and modular spaces, Springer-Verlag, Berlin, 1983.
12. p(x) on which the Hardy-Littlewood maximal operator is not bounded, Expo. Math. 19 (2001), no. 4, 369-371.
13. MICHAEL RŮŽIČCA, Electrorheological fluids: modeling and mathematical theory, Springer-Verlag, Berlin, 2000.
14. n), Dokl. Akad. Nauk 369 (1999), no. 4, 451-454.
15. n), Integral Transform. Spec. Funct. 7 (1998), no. 3-4, 261-284.
16. ELIAS M. STEIN, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, N.J., 1970.
17. V. V. ZHIKOV, Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), no. 4, 675-710, 877.
18. _, Meyer-type estimates for solving the nonlinear Stokes system, Differ. Uravn. 33 (1997), no. 1, 107-114, 143.
19. VASILIǏ V. ZHIKOV, On Lavrentiev's phenomenon, Russian J. Math. Phys. 3 (1995), no. 2, 249-269.