For and , the -th order maximal commutator of the singular integral operator with rough variable kernels is defined by
In this paper the authors prove that the -th order maximal commutator is a bounded operator on if satisfies the same conditions given by Calderón and Zygmund. Moreover, the -boundedness of the -th order commutator of the rough maximal operator with variable kernel, which is defined by
is also given here. These results obtained in this paper are substantial improvement and extension of some known results.
Cite this article
Yanping Chen, Yong Ding, Ran Li, boundedness for maximal commutators with rough variable kernels. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 361–391DOI 10.4171/RMI/640