Péter Kórus

On the uniform convergence of double sine series with generalized monotone coefficients

Chaundy and Jolliffe proved their classical theorem on the uniform convergence of sine series with monotone coefficients in 1916. Lately, it has been generalized using classes MVBVS and SBVS2 instead of monotone sequences. In two variables, the class MVBVDS was studied under the uniform regular convergence of double sine series. We shall generalize those results defining a new class of double sequences for the coefficients.

Necessary and Sufficient Conditions for the L 1 -Convergence of Double Fourier Series

We extend the results of paper of F.Móricz (2010), where necessary conditions were given for the L1-convergence of double Fourier series. We also give necessary and sufficient conditions for the L1-convergence under appropriate assumptions.