Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series (Q2915441)
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scientific article; zbMATH DE number 6083272
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series |
scientific article; zbMATH DE number 6083272 |
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Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series (English)
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17 September 2012
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Walsh function
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pointwise summability
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Marcinkiewicz-Fejér means
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Lebesgue points
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Marcinkiewicz proved that the two-dimensional classical trigonometric Marcinkiewicz-Fejér means of a function in the logarithm space converge a.e.\ to the function itself. Analogous results exist for Walsh-Fourier series, due to Weisz.NEWLINENEWLINE The present authors characterize the set of convergence of the Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series. They introduce the Marcinkiewicz-Lebesgue points and prove that a.e.\ point is a Marcinkiewicz-Lebesgue point of an integrable function \(f\) and the Marcinkiewicz-Fejér means of the two-dimensional Walsh-Fourier series of \(f\) converge to \(f\) at each Marcinkiewicz-Lebesgue point.
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