Abstract. We give necessary and sufficient conditions in order that the sum of a double cosine series with nonnegative coefficients belong to the two-dimensional Zygmund classes $\Lambda_*(2)$ or $\lambda_*(2)$, respectively. Our theorem is the extension of the corresponding theorem by Boas from single to double cosine series.

AMS Subject Classification (1991): 42B05, 42A16

Keyword(s): cosine series, \Lambda_*, \lambda_*, Zygmund classesand, summation by parts

Received February 6, 2003, and in revised form April 11, 2003. (Registered under 5801/2009.)