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  • 1 University of Szeged Bolyai Institute Aradi vértanúk tere 1 Szeged 6720 Hungary
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We introduce the higher order Lipschitz classes Λr(α) and λr(α) of periodic functions by means of the rth order difference operator, where r = 1, 2, ..., and 0 < αr. We study the smoothness property of a function f with absolutely convergent Fourier series and give best possible sufficient conditions in terms of its Fourier coefficients in order that f belongs to one of the above classes.