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

Huoxiong Wu¹

¹ School of Mathematical Sciences Xiamen University Xiamen 361005 People's Republic of China

Studia Mathematica, Tome 167 (2005) no. 1, pp. 29-43

Résumé

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.

Détail

DOI : 10.4064/sm167-1-3

Keywords: author studies commutators generated suitable function mathbb oscillatory singular integral rough kernel mit omega polynomial phase where mit omega homogeneous degree zero mathbb bmo function lipschitz function mapping properties these higher order commutators mathbb which essential improvements known results given