# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Boundedness of higher order commutators of oscillatory singular integrals with rough kernels

### Tom 167 / 2005

Studia Mathematica 167 (2005), 29-43 MSC: 42B20, 42B25. DOI: 10.4064/sm167-1-3

#### Streszczenie

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.

#### Autorzy

• Huoxiong WuSchool of Mathematical Sciences
Xiamen University
Xiamen 361005
People's Republic of China
e-mail

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