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On integrability and strong summability of Walsh-Kaczmarz series

Об интегрируемости и сильной суммируемости рядов по системе Уолша-Качмажа

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Abstract

In this paper we are concerned with integrability conditions and strong convergence properties of Walsh-Kaczmarz series that are derived from an inequality with respect to Walsh-Kaczmarz-Dirichlet kernels. Such type of inequalities, called Sidon type inequlities, have already been known for several other systems. The trigonometric and the Walsh-Paley-systems are among them. They turned to be useful in several areas including integrability conditions, strong convergence, strong approximation, and multipliers.

абстрактный

В работе исследуются условия интегрируемости и свойства сильной суммируемости рядов по системе Уолша- Качмажа, которые выводятся из одного неравенства въшолненного для ядер Дирихле по ϧтой системе. Неравенства подобного типа, известные как оценки типа Сидона, были известны для некоторых других систем, в частности, тригонометрической и Уолша в нумерации Пϧли. ϑти неравенства оказываются полезным инструментом во многих напаравлениях, например, при изучении условий интегрируемости, свойств сильной сходимости и сильной аппроксимации, а также мульипликаторов.

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  1. Department of Numerical Analysis, Eötvös L. University, Pázmány P. sétány 1/C, 1117, Budapest, Hungary

    S. Fridli

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Fridli, S. On integrability and strong summability of Walsh-Kaczmarz series. Anal Math 40, 197–214 (2014). https://doi.org/10.1007/s10476-014-0303-7

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  • DOI: https://doi.org/10.1007/s10476-014-0303-7

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