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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Order summability of multiple Fourier series


Authors: G. E. Peterson and G. V. Welland
Journal: Trans. Amer. Math. Soc. 205 (1975), 221-246
MSC: Primary 42A92
DOI: https://doi.org/10.1090/S0002-9947-1975-0374807-3
MathSciNet review: 0374807
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Abstract: Jurkat and Peyerimhoff have characterized monotone Fouriereffective summability methods as those which are stronger than logarithmic order summability. Here the analogous result for double Fourier series is obtained assuming unrestricted rectangular convergence. It is also shown that there is a class of order summability methods, which are weaker than any Cesàro method, for which the double Fourier series of any $ f \in L$ is restrictedly summable almost everywhere. Finally, it is shown that square logarithmic order summability has the localization property for exponentially integrable functions.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0374807-3
Keywords: Logarithmic order summability, multiple Fourier series, order summability, restricted rectangular convergence, localization, exponentially integrable, maximal function
Article copyright: © Copyright 1975 American Mathematical Society

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