Abstract view
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Compactness of Hardy-Type Operators over Star-Shaped Regions in $\mathbb{R}^N$
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Published:2004-12-01
Printed: Dec 2004
Pankaj Jain
Pawan K. Jain
Babita Gupta
Abstract
We study a compactness property of the operators between weighted
Lebesgue spaces that average a function over certain domains involving
a star-shaped region. The cases covered are (i) when the average is
taken over a difference of two dilations of a star-shaped region in
$\RR^N$, and (ii) when the average is taken over all dilations of
star-shaped regions in $\RR^N$. These cases include, respectively,
the average over annuli and the average over balls centered at origin.
