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A Note on Convergence of Fourier Series of a Function on Wiener's Class Vp
Published online by Cambridge University Press: 20 November 2018
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Let f be a 2π-periodic function defined on [0, 2π]. We set
where suprema have been taken with respect to all partitions P:a = t0<t1<t2<…<tn<=b of any segment [a, b] contained in [0, 2π]. We call the pth total variation of f on [a, b]. If we denote pth total variaiton of f on [0, 2π] by Vp(f), then we can define Wiener's class simply by
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