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Abstract. We give necessary and sufficient coefficient conditions under which the sum of a double sine or cosine-sine series with nonnegative coefficients belong to the two-dimensional Zygmund classes $\Lambda_*(2)$ or $\lambda_*(2)$, respectively. Our theorems are the extensions of the corresponding theorems by Boas and by Németh from single to double series.
AMS Subject Classification
(1991): 42B05, 42A16
Keyword(s):
cosine series,
sine series,
\Lambda_*,
\lambda_*,
Zygmund classesand,
summation by parts
Received June 11, 2003. (Registered under 5802/2009.)
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