On \((C,1)\) summability for Vilenkin-like systems (Q2717550)
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scientific article; zbMATH DE number 1605149
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \((C,1)\) summability for Vilenkin-like systems |
scientific article; zbMATH DE number 1605149 |
Statements
17 June 2001
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Walsh system
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\((C,1)\)-means
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Vilenkin-like systems
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group of 2-adic integers
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UDMD systems
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On \((C,1)\) summability for Vilenkin-like systems (English)
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The Fourier series of integrable functions with respect to Vilenkin-like orthonormal systems are considered. It is proved that the maximal operator of the \((C,1)\)-means is of weak tye \((1,1)\). Hence the \((C,1)\)-means of an integrable function converge to the function a.e. The Vilenkin-like systems are generalizations of the Walsh- and Vilenkin systems, the character system of the group of 2-adic integers and the UDMD systems.
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