Abstract
The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.
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R. Coifman, R. Rochberg and G. Weiss: Factorization theorems for Hardy spaces in several variables. Ann. of Math. 123 (1976), 611–635.
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.
L. Diening: Maximal function on generalized Lebesgue spaces L p(·). Math. Inequal. Appl. 7 (2004), 245–253.
L. Diening and M. Růžička: Calderón-Zygmund operators on generalized Lebesgue spaces L p(·) and problems related to uid dynamics. J. Reine Angew. Math. 563 (2003), 197–220.
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.
S. Janson: Mean oscillation and commutators of singular integral operators. Ark. Mat. 16 (1978), 263–270.
A. Karlovich and A. Lerner: Commutators of singular integrals on generalized L p spaces with variable exponent. Publ. Nat. 49 (2005), 111–125.
V. Kokilashvili and S. Samko: Maximal and fractional operators in weighted L p(x) spaces. Revista Mat. Iberoam. 20 (2004), 493–515.
O. Kovacik and J. Rákosník: On spaces L p(x) and W k,p(x). Czech. Math. J. 41 (1991), 592–618.
A. Lerner: Weighted norm inequalities for the local sharp maximal function. J. Fourier Anal. Appl. 10 (2004), 465–474.
B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226.
J. Musielak: Orlicz spaces and Modular spaces. Lecture Notes in Mathematics, 1034, Springer-Verlag, Berlin, 1983.
A. Nekvinda: Hardy-Littlewood maximal operator on L p(x) (ℝn). Math. Inequal. Appl. 7 (2004), 255–265.
C. Perez: Endpoint estimates for commutators of singular integral operators. J. Funct. Anal. 128 (1995), 163–185.
C. Perez and R. Trujillo-Gonzalez: Sharp weighted estimates for multilinear commutators. J. London Math. Soc. 65 (2002), 672–692.
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.
M. Růžička: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, 2000.
E. Stein: Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integral. Princeton University Press. Princeton, NJ, 1993.
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Xu, Js. The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent. Czech Math J 57, 13–27 (2007). https://doi.org/10.1007/s10587-007-0040-1
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DOI: https://doi.org/10.1007/s10587-007-0040-1