Spherical maximal operator on symmetric spaces of constant curvature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

Spherical maximal operator on symmetric spaces of constant curvature

Authors:	Amos Nevo P K Ratnakumar

Institution:	Institute of advanced studies in mathematics, Technion--Israel Institute of Technology, Haifa 32900, Israel ; Institute of advanced studies in mathematics, Technion--Israel Institute of Technology, Haifa 32900, Israel

Abstract:	We prove an endpoint weak-type maximal inequality for the spherical maximal operator applied to radial funcions on symmetric spaces of constant curvature and dimension $n\ge 2$ . More explicitly, in the Lorentz space associated with the natural isometry-invariant measure, we show that, for every radial function , $\begin{displaymath}\Vert{\mathcal M}f\Vert _{\,n^{\prime},\infty}\leq C_n \Vert f \Vert _{n^{\prime},1},\,\,\,\, n^\prime=\frac{n}{n-1}.\end{displaymath}$ The proof uses only geometric arguments and volume estimates, and applies uniformly in every dimension.

Keywords:	Symmetric spaces constant curvature spherical means maximal function

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