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Compactness of Hardy-Type Operators over Star-Shaped Regions in ${{\mathbb{R}}^{N}}$
Published online by Cambridge University Press: 20 November 2018
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 ${{\mathbb{R}}^{N}}$, and (ii) when the average is taken over all dilations of star-shaped regions in ${{\mathbb{R}}^{N}}$. These cases include, respectively, the average over annuli and the average over balls centered at origin.
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- Copyright © Canadian Mathematical Society 2004
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