Higher order Lipschitz classes of functions and absolutely convergent Fourier series |
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| Authors: | Ferenc Móricz |
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| Affiliation: | (1) Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720, Hungary |
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| Abstract: | We introduce the higher order Lipschitz classes Λ r (α) and λ r (α) of periodic functions by means of the rth order difference operator, where r = 1, 2, ..., and 0 < α ≦ r. 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. This research was supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192. |
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| Keywords: | KeywordHeading" > and phrases absolutely convergent Fourier series rth modulus of smoothness Lipschitz classes Λ r (α ) and λ r (α ) for r = 1, 2, ... and 0 < α ≦ r |
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