A Note on Weak Type $(1,1)$ Estimate for the Higher Order Commutators of Christ-Journé Type

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Year: 2019

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 268–287

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 $m_{x,y}a_i=\int_0^1a_i(sx+(1-s)y)ds$ .

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

Pages: 20

A Note on Weak Type (1,1)(1,1) Estimate for the Higher Order Commutators of Christ-Journé Type