Abstract
In this paper we study the (L p(u p),L q(v q)) boundedness of the higher order commutatorsT m Ω,α,b andM m Ω,α,b formed by the fractional integral operatorT Ω,α , the fractional maximal operatorM Ω,α , and a functionb(x) in BMO(v), respectively.
Our results imporve and extend the corresponding results obtained by Segovia and Torrea in 1993 [9].
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Chanillo, S., Watson, D. andWheeden, R. L., Some integral and maximal operators related to star like sets,Studia Math. 107 (1993), 223–255.
Ding, Y., Weighted boundedness for commutators of integral operators of fractionnal order with rough kernels,Beijing Shifan Daxue Xuebao 32 (1996), 157–161 (Chinese).
Ding, Y., Weighted boundedness for commutators of a class of rough maximal operators,Kexue Tongbao (Chinese) 41 (1996), 385–388 (Chinese).
Ding, Y., Weak type bounds for a class of rough operators with power weights,Proc. Amer. Math. Soc. 125 (1997), 2939–2942.
Ding, Y. andLu, S. Z., Weighted norm inequalities for fractional integral operators with rough kernel,Canad. J. Math. 50 (1998), 29–39.
García-Cuerva, J. andRubio de Francia, J. L.,Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985.
Hedberg, L. I., On certain convolution inequalities,Proc. Amer. Math. Soc. 36 (1972), 505–510.
Muckenhoupt, B. andWheeden, R. L., Weighted norm inequalities for singular and fractional integrals,Trans. Amer. Math. Soc. 161 (1971), 249–258.
Segovia, C. andTorrea, J. L., Higher order commutators for vector-valued Calderón-Zygmund operators,Trans. Amer. Math. Soc. 336 (1993), 537–556.
Welland, G. V., Weighted norm inequalities for fractional integrals,Proc. Amer. Math. Soc. 51 (1975), 143–148.
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The project was supported by NNSF of China.
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Ding, Y., Lu, S. Higher order commutators for a class of rough operators. Ark. Mat. 37, 33–44 (1999). https://doi.org/10.1007/BF02384827
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DOI: https://doi.org/10.1007/BF02384827