@Article{ATA-35-268,
author = {Yong Ding and Xudong Lai},
title = {A Note on Weak Type $(1,1)$ Estimate for the Higher Order Commutators of Christ-Journé Type},
journal = {Analysis in Theory and Applications},
year = {2019},
volume = {35},
number = {3},
pages = {268--287},
abstract = {<p style="text-align: justify;">In this paper, a weak type $(1,1)$ estimate is established for the higher order commutator introduced by Christ and Journé which is defined by</p><p style="text-align: justify;">$$ T[a_1,\cdots,a_l]f(x)=p.v. \int_{R^d} K(x-y)\Big(\prod_{i=1}^lm_{x,y}a_i\Big)\cdot f(y)dy, $$</p><p style="text-align: justify;">where $K$ is the standard Calderόn-Zygmund convolution kernel on $\mathbb{R}^d (d\geq2)$ and $m_{x,y}a_i=\int_0^1a_i(sx+(1-s)y)ds$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-0007},
url = {http://global-sci.org/intro/article_detail/ata/13116.html}
}