Strong convergence theorem for Walsh-Marcinkiewicz means (Q2794813)
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scientific article; zbMATH DE number 6554485
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong convergence theorem for Walsh-Marcinkiewicz means |
scientific article; zbMATH DE number 6554485 |
Statements
Strong convergence theorem for Walsh-Marcinkiewicz means (English)
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11 March 2016
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Marcinkiewicz means
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Walsh-Fourier series
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dyadic Hardy space
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strong convergence
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0.9514954
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0.9490419
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0.9118812
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0.9115838
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0.90701437
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0.8754679
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0.87501276
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It is known that the maximal operator of the Marcinkiewicz means of the two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space \(H_p\) to \(L_p\) if \(2/3<p<\infty\) and it is not bounded if \(0<p\leq 2/3\). In this paper a strong convergence theorem is proved for the Marcinkiewicz means in \(H_{2/3}\).
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