Boundedness of higher order commutators of oscillatory singular integrals with rough kernels
Volume 167 / 2005
Studia Mathematica 167 (2005), 29-43
MSC: 42B20, 42B25.
DOI: 10.4064/sm167-1-3
Abstract
The author studies the commutators generated by a suitable function $a(x)$ on ${{{{\mathbb R}}}^n}$ and the oscillatory singular integral with rough kernel ${\mit \Omega }(x)|x|^n$ and polynomial phase, where ${\mit \Omega }$ is homogeneous of degree zero on ${{{{\mathbb R}}}^n}$, and $a(x)$ is a BMO function or a Lipschitz function. Some mapping properties of these higher order commutators on $L^p({{{{\mathbb R}}}^n})$, which are essential improvements of some well known results, are given.
