Abstract. We investigate the order of magnitude of the modulus of continuity of a function $f(x,y)$ with absolutely convergent double Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that $f$ belong to one of the generalized Lipschitz classes Lip($\alpha, \beta; L$) and Lip($\alpha, \beta; 1/L$), where $0 \leq\alpha, \beta\leq 1$, $L=L(x,y)=L_1(x) L_2(y)$ is positive and $L_1(x)$ and $L_2(y)$ are non-decreasing, slowly varying functions such that $L_1(x), L_2(y) \rightarrow\infty $ as $x,y \rightarrow\infty $. These sufficient conditions are also necessary in the case of a certain subclass of Fourier coefficients.

AMS Subject Classification (1991): 42B99, 42A32, 26A15

Keyword(s): Fourier series, absolute convergence, multiplicative modulus of continuity, generalized multiplicative Lipschitz classes

Received October 7, 2008, and in revised form January 20, 2009. (Registered under 6431/2009.)