On the uniform convergence of double sine series with generalized monotone coefficients
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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.
Key words and phrasessine series double sine series Fourier series uniform convergence regular convergence generalized monotonicity mean value bounded variation supremum bounded variation
Mathematics subject classification numbers42A20 42A32 42B99
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