Geodesic
Compactness of Hardy-Type Operators over Star-Shaped Regions in ${{\mathbb{R}}^{N}}$
Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 540-552

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DOI

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.
DOI : 10.4153/CMB-2004-053-5
Mots-clés : 46E35, 26D10, Hardy operator, Hardy-Steklov operator, compactness, boundedness, star-shaped regions 
Jain, Pankaj; Jain, Pawan K.; Gupta, Babita. Compactness of Hardy-Type Operators over Star-Shaped Regions in ${{\mathbb{R}}^{N}}$. Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 540-552. doi: 10.4153/CMB-2004-053-5
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     title = {Compactness of {Hardy-Type} {Operators} over {Star-Shaped} {Regions} in ${{\mathbb{R}}^{N}}$},
     journal = {Canadian mathematical bulletin},
     pages = {540--552},
     year = {2004},
     volume = {47},
     number = {4},
     doi = {10.4153/CMB-2004-053-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-053-5/}
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