Weak type (1,1) bound criterion for singular integral with rough kernel and its applications
Classical Analysis and ODEs
2017-08-15 v2
Abstract
In this paper, a weak type (1,1) bound criterion is established for singular integral operator with rough kernel. As some applications of this criterion, we prove some important operators with rough kernel in harmonic analysis, such as Calder\'on commutator, higher order Calder\'on commutator, general Calder\'on commutator, Calder\'on commutator of Bajsanski-Coifman type and general singular integral of Muckenhoupt type, are all of weak type (1,1).
Keywords
Cite
@article{arxiv.1509.03685,
title = {Weak type (1,1) bound criterion for singular integral with rough kernel and its applications},
author = {Yong Ding and Xudong Lai},
journal= {arXiv preprint arXiv:1509.03685},
year = {2017}
}
Comments
27 pages. To appear in Trans. Amer. Math. Soc