The maximal operator of Bochner-Riesz means for radial functions (Q2712540)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The maximal operator of Bochner-Riesz means for radial functions |
scientific article |
Statements
8 January 2002
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maximal operator
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Bochner-Riesz means
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radial function
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Lebesgue space
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The maximal operator of Bochner-Riesz means for radial functions (English)
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Let NEWLINE\[NEWLINES^\delta_\ast f(x)=\sup_{\varepsilon>0}(2\pi)^{-n} \left|\int_{{\mathbb{R}}^n}(1-|\varepsilon\xi|^2)^\delta_+\hat f(\xi) e^{i\langle x,\xi\rangle} d\xi\right|.NEWLINE\]NEWLINE The author proves that for \(n\geq 2\), \(0<\delta\leq (n-2)/2\) and \(p=2n/(n+1+2\delta)\), then \(S^\delta_\ast\) is of weak type \((p,p)\) on radial functions in \(L^p({\mathbb{R}}^n)\).
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