Almost everywhere convergence of the spherical partial sums for radial functions (Q1100379)
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scientific article; zbMATH DE number 4042509
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Almost everywhere convergence of the spherical partial sums for radial functions |
scientific article; zbMATH DE number 4042509 |
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Almost everywhere convergence of the spherical partial sums for radial functions (English)
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1988
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Let \(f\in L^ p(R^ n)\), \(n\geq 2\), be a radial function and let \(S_ Rf\) be the spherical partial sums operator. We prove that if \(2n/n+1<p<2n/n-1\) then \(S_ Rf(x)\to f(x)\) a.e. as \(R\to \infty\). The result is false for \(p<2n/n+1\) and \(p>2n/n-1\).
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radial function
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