On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent

Zeitschrift für Analysis und ihre Anwendungen

Volumn 22, Issue 4, 2003, Pages 899-910

  Kokilashvili, V ^a   Samko, S ^b  

^a A RAZMADZE MATHEMATICAL INSTITUTE   (Georgia)

^b UNIVERSITY OF ALGARVE   (Portugal)

Author keywords

Lebesgue spaces; Maximal function; Riesz potential; Variable exponent; Weighted estimates

Indexed keywords

EID: 1342283933     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/1178     Document Type: Article

References (21)

1. Adams, R. A. and L. I. Hedberg: Function Spaces and Potential Theory. Berlin: Spinger-Verlag 1996.
2. p spaces. Ann. Acad. Sci. Fennicae, Math. 28 (2003), 223 - 238.
3. p(̇). Preprint. Freiburg (Germany): Math. Fak., Albert-Ludwigs-Univ. 2002.
4. k,p(̇). Preprint. Freiburg (Germany): Math. Fak., Albert-Ludwigs-Univ. 22/2002, 15.07.2002, 1 - 13.
5. p(̇). Math. Inequ. Appl 2003 (to appear).
6. p(x) and problems related to fluid dynamics. Preprint. Frteiburg (Germany): Math. Fak., Albert-Ludwigs-Univ. 21/2002, 04.07.2002, 1 -20.
7. p(x). Math. Inequ. Appl. 5 (2002), 235 - 235.
8. p(x) spaces. Z. Anal. Anw. 21 (2002), 681 - 690.
9. k,p(x)(ω). Proc. Royal Soc. London 437 (1992), 229 - 236.
10. Fiorenza, A: A mean continuity type result for certain Sobolev spaces with variable exponent. Commun. Contemp. Math. 4 (2002), 587 - 605.
11. p(x) spaces. Revista Mat. Iberoamer. (to appear).
12. Kokilashvili, V. and S. Samko: Singular integrals and potentials in some Banach spaces with variable exponent. Proc. A. Razmadze Math. Inst. 129 (2002), 150 -155.
13. Kokilashvili, V. and S. Samko: Singular integrals in weighted Lebesgue spaces with variable exponent. Georgian Math. J. 10 (2003), 145 - 156.
14. Kokilashvili, V. S. and Samko: Singular integrals in weighted Lebesgue spaces with variable exponent. Preprint. Lisbon: Inst. Superior Técnico, Dep. de Mat. (30): 1 - 16, December 2002.
15. Kokilashvili V, and S. Samko: Singular integrals in weighted Lebesgue spaces with variable exponent. Preprint. Lisbon: Inst. Superior Técnico, Dep. de Mat. (24): 1 - 24, December 2002.
16. k,p(x). Czechoslovak Math. J. 41 (116) (1991), 592 - 618.
17. Růžička, M: Electroreological Fluids: Modeling and Mathematical Theory. Lect. Notes Math. 1748 (2000).
18. p(x). Int, Transf. & Special Funct. 7 (1998), 261 - 284.
19. p(x), Int. Transf. & Special Funct. 7 (1998), 123 - 144.
20. p(x). Contemp. Math 212 (1998), 203 - 219.
21. P(t) ([0, 1]) (in Russian). Mat. Zam. 26 (1979), 613 - 632.