Year: 2019
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 268–287
Abstract
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
$$ T[a_1,\cdots,a_l]f(x)=p.v. \int_{R^d} K(x-y)\Big(\prod_{i=1}^lm_{x,y}a_i\Big)\cdot f(y)dy, $$
where $K$ is the standard Calderόn-Zygmund convolution kernel on $\mathbb{R}^d (d\geq2)$ and $m_{x,y}a_i=\int_0^1a_i(sx+(1-s)y)ds$.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0007
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 268–287
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Weak type $(1 1)$ higher order commutator.