Singular integrals generated by zonal measures期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Singular integrals generated by zonal measures

Authors:	Dmitry Ryabogin Boris Rubin

Institution:	Department of Mathematics, University of Missouri, Columbia, Missouri 65211 ; Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

Abstract:	We study -mapping properties of the rough singular integral operator $T_\nu f(x)=\int_0^\infty dr/r \int_{\Sigma_{n - 1}} f(x-r\theta)d\nu(\theta)$ depending on a finite Borel measure $\nu$ on the unit sphere $\Sigma_{n -1}$ in $\mathbb{R}^n$ . It is shown that the conditions $\sup_{\vert\xi \vert=1} \int_{\Sigma_{n -1}} \log (1/\vert \theta \cdot \xi \vert) d\vert\nu\vert(\theta) < \infty$ , $\nu(\Sigma_{n - 1})=0$ imply the -boundedness of $T_\nu$ for all $1<p<\infty$ provided that and $\nu$ is zonal.

Keywords:	Singular integrals $L^p$-boundedness

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文