Two operators related to Marcinkiewicz integrals

• DOI: 10.1007/s10114-009-8038-2
• Publication Date: 2009-10-15T03:03:48Z
• Authors: Hui Xia Mo; Shan Zhen Lu
• Keywords: Commutator; Zero (linguistics); Singular integral operators; Degree (music)

In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral \( \mu _\Omega ^{\vec b} \) , multilinear Marcinkiewicz integral μΩA and its variation \( \tilde \mu _\Omega ^A \) on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of Ls-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces.