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. 128 369 – 380 10.1007/s10474-010-9217-4 . [2] Móricz , F. 2009 On the uniform convergence of sine integrals J. Math. Anal

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Abstract  

We study the uniform convergence of Walsh-Fourier series of functions on the generalized Wiener class BV (p(n)↑∞)

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The almost uniform convergence is between uniform and quasi-uniform one. We give some necessary and sufficient conditions under which the almost uniform convergence coincides on compact sets with uniform, quasi-uniform or uniform convergence, respectively. In the second section continuity of almost uniform limits is considered. Finally we characterize the set of all points at which a net of functions is almost uniformly convergent to a given function.

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Abstract  

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.

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] Goginava , U. , On the uniform convergence of Walsh-Fourier series , Acta Math. Hungar. , 93 ( 1–2 ) ( 2001 ), 59 – 70 . [10

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uniform convergence of sequences of certain linear operators, Acta Math. Hungar. , 91 (2001), no. 1–2, 159–186. MR 2004d :42010 Vértesi P. On uniform convergence of

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