ACTA issues

## Double sine and cosine-sine series with nonnegative coefficients

Vanda Fülöp

Acta Sci. Math. (Szeged) 70:1-2(2004), 101-116
5802/2009

 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.)