Abstract
In this paper, weighted inequalities for a certain general commutator associated to a singular integral operator satisfying a variant of Ho¨ rmander’s condition on Lebesgue spaces are obtained. To do this, some weighted sharp maximal function inequalities for the commutator are proved.
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References
J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics (North- HollandMath., Amsterdam, 1985), Vol. 16.
E. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals (Princeton Univ. Press, Princeton, NJ, 1993).
R. Coifman, R. Rochberg, and G. Weiss, “Factorization theorems for Hardy spaces in several variables,” Ann. of Math. 103 (5), 611–635 (1976).
C. Pérez and R. Trujillo-Gonzalez, “Sharp weighted estimates for multilinear commutators,” J. London Math. Soc. 65 (6), 672–692 (2002).
S. Chanillo, “A note on commutators,” Indiana Univ. Math. J. 31 (1), 7–16 (1982).
S. Janson, “Mean oscillation and commutators of singular integral operators,” Ark. Math. 16 (2), 263–270 (1978).
M. Paluszynski, “Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg, and Weiss,” Indiana Univ. Math. J. 44 (1), 1–17 (1995).
S. Bloom, “A commutator theorem and weighted BMO,” Trans. Amer. Math. Soc. 292 (1), 103–122 (1985).
B. Hu and J. Gu, “Necessary and sufficient conditions for boundedness of some commutators with weighted Lipschitz spaces,” J. of Math. Anal. and Appl. 340 (5), 598–605 (2008).
S. Krantz and S. Li, “Boundedness and compactness of integral operators on spaces of homogeneous type and applications,” J. of Math. Anal. Appl. 258 (5), 629–641 (2001).
Y. Lin and S. Lu, “Toeplitz type operators associated to strongly singular integral operator,” Sci. in China (Ser. A) 36 (5), 615–630 (2006).
S. Lu and H. Mo, “Toeplitz type operators on Lebesgue spaces,” Acta Math. Scientia 29(B) (1), 140–150 (2009).
D. Grubb and C. Moore, “a variant of Hörmander’s condition for singular integrals,” Colloq. Math. 73 (2), 165–172 (1997).
R. Trujillo-Gonzalez, “Weighted norm inequalities for singular integral operators satisfying a variant of Hörmander’s condition,” Comment. Math. Univ. Carolin. 44 (1), 137–152 (2003).
J. Garcia-Cuerva, “Weighted H p spaces,” Dissert. Math. 162 (1), 1–56 (1979).
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Hu, H., Liu, L. Weighted inequalities for a general commutator associated to a singular integral operator satisfying a variant of Hörmander’s condition. Math Notes 101, 830–840 (2017). https://doi.org/10.1134/S0001434617050091
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DOI: https://doi.org/10.1134/S0001434617050091