Abstract
In this paper we give the (L p(ωp), L q(ωq)) boundedness for a class of multilinear operators, which is simular to the higher-order commutator for the rough fractional integral. In our results the kernel function is merely assumed on a size condition.
Similar content being viewed by others
References
B. Bajsanski, R. Coifman, On singular integrals, Proc. Symp. Pure Math., Amer. Math. Soc. Providence, R. I., 1967, 10:1–17
J. Cohen, A sharp estimate for a multilinear singular integral in ℝn, Indiana Unit. Math. Jour., 1981, 30:693–702
J. Cohen, J. Gosselin, A BMO estimate for a multilinear singular integrals, Illinois Jour. Math., 1986, 30:445–464
S. Hofmann, On some nonstandard Calderón-Zygmund operators, Studia Math., 1994, 109:105–131
Y. Ding, S. Z. Lu, Weighted norm inequalities for fractional integral operators with rough kernel, Canad. Jour. Math., 1998, 50:29–39
Y. Ding, Weak type bounds for a class of rough operators with power weights, Proc. Amer. Math. Soc., 1997, 125:2939–2942
Y. Ding, Weighted boundedness of commutators for a class of rough maximal operators, (in Chinese), Ke Xue Tong Bao, 1996, 41:385–388
Y. Ding, On the commutators for a class of rough operators, (in Chinese), Chinese Ann. Math., 1998, 19(A):367–372
J. Garcia-Cuerva, J. L. Rubio de Francia, Weighted norm inequalities and relanted topics, North-Holland, Amsterdam, 1985
L. I. Hedberg, On certain convolution inequalities, Proc. Amer. Math. Soc., 1972, 36:505–510
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by the NNSF (Grant: 19971010) and National 973 Project of China.
Rights and permissions
About this article
Cite this article
Ding, Y., Lu, S.Z. Weighted Boundedness for a Class of Rough Multilinear Operators. Acta Math Sinica 17, 517–526 (2001). https://doi.org/10.1007/s101140100113
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s101140100113