Abstract
Let [b, T] be the commutator generated by a Lipschitz function b ∈ Lip(β)(0 < β < 1) and multiplier T. The authors studied the boundedness of [b, T] on the Lebesgue spaces and Hardy spaces.
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Alvarez, J., Bagby, R., Kurtz, D.S., Pérez, C. Weighted estimates for commutators of linear operators. Studia Math., 104: 195–209 ( 1993)
Calderon, A.P., Torchinsky, A. Parabolic maximal functions associated with a distribution, II. Adv. Math., 24: 101–171 (1977)
Chanillo, S. A note on commutators. Indiana Univ. Math. J., 31: 7–16 (1982)
Coifman, R., Rochberg, R., Weiss, G. Factorization theorems for Hardy spaces in several variables. Ann. Math., 103: 611–635 (1976)
Fefferman C., Stein, E.M. H p spaces of several variables. Acta Math., 129: 137–193 (1972)
Hörmander, L. Estimate for translation invariant operators in L p spaces. Acta Math., 104: 93–139 (1960)
Janson, S. Mean oscillation and commutators of singular integral operators. Ark. Math., 16: 263–270 (1978)
Kurtz, D.S., Wheeden, R.L. Results on weighted norm inequalities for multipliers. Tran. Amer. Math. Soc., 255: 343–362 (1979)
Lu, S.Z., Wu, Q., Yang, D.C. Boundedness of commutators on Hardy type spaces. Science in China, 45: 984–997 (2002)
Muckenhoupt, B., Wheeden, R.L. Weighted norm inequalities for fractional integrals. Tran. Amer. Math. Soc., 192: 261–274 (1974)
Paluszyński, M. Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ. Math. J., 44: 1–17 (1995)
Pérez, C. Endpoint estimates for commutators of singular integral operators. J. Funct. Anal., 128: 163–185 (1995)
Stein, E.M. Harmonic Analysis: Real-variable methods, orthogonality, and oscillatory integrals. Princetion Univ Press, Princetion, NJ, 1993
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Supported by National 973 project (G.19990751) and the Doctoral Programme Foundation of Institution of Higher Education of China(20040027001).
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Li, Wm., Lu, Sz. & Mo, Hx. The Boundedness for Commutators of Multipliers. Acta Mathematicae Applicatae Sinica, English Series 23, 113–122 (2007). https://doi.org/10.1007/s10255-006-0355-y
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DOI: https://doi.org/10.1007/s10255-006-0355-y