Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series and Hardy spaces (Q2911326)
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scientific article; zbMATH DE number 6074637
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series and Hardy spaces |
scientific article; zbMATH DE number 6074637 |
Statements
30 August 2012
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Marcinkiewicz-Fejér means
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Walsh-Kaczmarz series
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Hardy spaces
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atomic decomposition
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Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series and Hardy spaces (English)
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It is known that the maximal Marcinkiewicz operator is bounded from the Hardy space \(H_p\) to \(L_p\), for both the Walsh and the Walsh-Kaczmarz series if \(p>2/3\). If \(p\leq 2/3\), this is not true.NEWLINENEWLINEIn this paper it is proved that the conjugate Marcinkiewicz-Fejér means of the Walsh-Kaczmarz series are uniformly bounded from \(H_p\) to \(H_p\) for \(p>2/3\). Moreover, a counterexample is given if \(p\leq 2/3\).
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