Double sine series with nonnegative coefficients and Lipschitz classes
Volume 105 / 2006
Colloquium Mathematicum 105 (2006), 25-34
MSC: 42B05, 42A16.
DOI: 10.4064/cm105-1-3
Abstract
Denote by $f_{\rm ss}(x,y)$ the sum of a double sine series with nonnegative coefficients. We present necessary and sufficient coefficient conditions in order that $f_{\rm ss}$ belongs to the two-dimensional multiplicative Lipschitz class ${\rm Lip}(\alpha ,\beta )$ for some $0<\alpha \le 1$ and $0<\beta \le 1.$ Our theorems are extensions of the corresponding theorems by Boas for single sine series.
