Geodesic
Approximation by M. Riesz's kernels in $L^p$ for $p1$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 5-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\alpha>0$. We consider the linear span ${\mathfrak X}_\alpha(\mathbb R^n)$ of scalar Riesz's kernels $\{\frac1{|x-a|^\alpha}\}_{a\in\mathbb R^n}$ and the linear span ${\mathfrak Y}_\alpha(\mathbb R^n)$ of vector Riesz's kernels $\{\frac1{|x-a|^{\alpha+1}}(x-a)\}_{a\in\mathbb R^n}$. We deal with the following questions. 1. When is the intersection ${\mathfrak X}_\alpha(\mathbb R^n)\cap L^p(\mathbb R^n)$ dense in $L^p(\mathbb R^n)$? 2. When is the intersection ${\mathfrak Y}_\alpha(\mathbb R^n)\cap L^p(\mathbb R^n,\mathbb R^n)$ dense in $L^p(\mathbb R^n,\mathbb R^n)$? 
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     title = {Approximation by {M.~Riesz's} kernels in $L^p$ for $p<1$},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a0/}
}
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A. B. Aleksandrov. Approximation by M. Riesz's kernels in $L^p$ for $p<1$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 5-38. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a0/

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