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Transactions of the American Mathematical Society

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

 

 

Lebesgue summability of double trigonometric series


Author: M. J. Kohn
Journal: Trans. Amer. Math. Soc. 225 (1977), 199-209
MSC: Primary 42A92
DOI: https://doi.org/10.1090/S0002-9947-1977-0425505-0
MathSciNet review: 0425505
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Abstract: We formulate a definition of symmetric derivatives of odd order for functions of two variables. Our definition is based on expanding in a Taylor's series a weighted average of the function about circles.

The definition is applied to derive results on Lebesgue summability for spherically convergent double trigonometric series.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0425505-0
Keywords: Multiple trigonometric series, spherically convergent series, symmetric derivative, symmetric approximate derivative, Lebesgue summability
Article copyright: © Copyright 1977 American Mathematical Society