ACTA issues

## Double cosine series with nonnegative coefficients

Vanda Fülöp

Acta Sci. Math. (Szeged) 70:1-2(2004), 91-100
5801/2009

 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.)