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.
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Dedicated to Professor József Szabados on the occasion of his seventieth birthday
This research was supported by the Hungarian National Foundation for Scientific Research under Grant T 046 192.
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Móricz, F. Higher order Lipschitz classes of functions and absolutely convergent Fourier series. Acta Math Hung 120, 355–366 (2008). https://doi.org/10.1007/s10474-007-7141-z
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DOI: https://doi.org/10.1007/s10474-007-7141-z
Key words 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