Keywords: commutator; Calderón-Zygmund singular integral; BMO; Lebesgue space with variable exponent; maximal function
@article{CMJ_2007_57_1_a1,
author = {Xu, Jing-shi},
title = {The boundedness of multilinear commutators of singular integrals on {Lebesgue} spaces with variable exponent},
journal = {Czechoslovak Mathematical Journal},
pages = {13--27},
year = {2007},
volume = {57},
number = {1},
mrnumber = {2309945},
zbl = {1174.42312},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a1/}
}
TY - JOUR AU - Xu, Jing-shi TI - The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent JO - Czechoslovak Mathematical Journal PY - 2007 SP - 13 EP - 27 VL - 57 IS - 1 UR - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a1/ LA - en ID - CMJ_2007_57_1_a1 ER -
Xu, Jing-shi. The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 13-27. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a1/
[1] R. Coifman, R. Rochberg and G. Weiss: Factorization theorems for Hardy spaces in several variables. Ann. of Math. 123 (1976), 611–635. | MR
[2] D. Cruz-Uribe, A. Fiorenza and C. Neugebauer: The maximal function on variable $L^p$ spaces. Ann. Acad. Sci. Fenn. Math. 28 (2003), 223–238. | MR
[3] L. Diening: Maximal function on generalized Lebesgue spaces $L^{p(\cdot )}$. Math. Inequal. Appl. 7 (2004), 245–253. | MR
[4] L. Diening and M. Růžička: Calderón-Zygmund operators on generalized Lebesgue spaces $L^{p(\cdot )}$ and problems related to fluid dynamics. J. Reine Angew. Math. 563 (2003), 197–220. | MR
[5] J. Garcia-Cuerva, E. Harboure, C. Segovia and J. Torrea: Weighted norm inequalities for commutators of strongly singular integrals. Indiana Univ. Math. J. 40 (1991), 1397–1420. | DOI | MR
[6] S. Janson: Mean oscillation and commutators of singular integral operators. Ark. Mat. 16 (1978), 263–270. | DOI | MR | Zbl
[7] A. Karlovich and A. Lerner: Commutators of singular integrals on generalized $L^p$ spaces with variable exponent. Publ. Nat. 49 (2005), 111–125. | MR
[8] V. Kokilashvili and S. Samko: Maximal and fractional operators in weighted $L^{p(x)}$ spaces. Revista Mat. Iberoam. 20 (2004), 493–515. | MR
[9] O. Kovacik and J. Rákosník: On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czech. Math. J. 41 (1991), 592–618. | MR
[10] A. Lerner: Weighted norm inequalities for the local sharp maximal function. J. Fourier Anal. Appl. 10 (2004), 465–474. | MR | Zbl
[11] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226. | DOI | MR | Zbl
[12] J. Musielak: Orlicz spaces and Modular spaces. Lecture Notes in Mathematics, 1034, Springer-Verlag, Berlin, 1983. | MR | Zbl
[13] A. Nekvinda: Hardy-Littlewood maximal operator on $L^{p(x)}(\mathbb{R}^n)$. Math. Inequal. Appl. 7 (2004), 255–265. | MR
[14] C. Perez: Endpoint estimates for commutators of singular integral operators. J. Funct. Anal. 128 (1995), 163–185. | DOI | MR | Zbl
[15] C. Perez and R. Trujillo-Gonzalez: Sharp weighted estimates for multilinear commutators. J. London Math. Soc. 65 (2002), 672–692. | DOI | MR
[16] L. Pick and M. Růžička: An example of a space $L^{p(x)}$ on which the Hardy-Littlewood maximal operator is not bounded. Expo. Math. 19 (2001), 369–371. | DOI | MR
[17] M. Růžička: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, 2000. | MR
[18] E. Stein: Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integral. Princeton University Press. Princeton, NJ, 1993. | MR