Weighted inequalities for a maximal function on the real line (Q2719732)
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scientific article; zbMATH DE number 1610112
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted inequalities for a maximal function on the real line |
scientific article; zbMATH DE number 1610112 |
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Weighted inequalities for a maximal function on the real line (English)
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5 February 2002
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Cesàro convergence
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maximal operator
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weights
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weighted inequalities
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The authors study maximal operators of the form NEWLINE\[NEWLINEM_{\alpha}f(x)=\sup_{R>0}{1\over (2R)^{1+\alpha}} \int_{R<|x-y|<2R} |f(y)|(|x-y|-R)^{\alpha}dy.NEWLINE\]NEWLINE This is done for \(-1<\alpha \leq 0\). They characterize the weights \(w\) for which the maximal operator \(M_\alpha\) is of weak, strong and restricted weak typ \((p,p)\) with respect to the measure \(w(x)dx\).
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