Compactness of Hardy-Type Operators over Star-Shaped Regions in $mathbb{R}^N$

Canadian mathematical bulletin

关键词: Hardy operator;    Hardy-Steklov operator;    compactness;    boundedness;    star-shaped regions;   

DOI  :  10.4153/CMB-2004-053-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We study a compactness property of the operators between weightedLebesgue spaces that average a function over certain domains involvinga star-shaped region. The cases covered are (i) when the average istaken over a difference of two dilations of a star-shaped region in$RR^N$, and (ii) when the average is taken over all dilations ofstar-shaped regions in $RR^N$. These cases include, respectively,the average over annuli and the average over balls centered at origin.

【 授权许可】

Unknown