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Fourier transforms of Dini-Lipschitz functions. (English) Zbl 0595.42006

Summary: It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f. In general, if f(x) belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms of f(x) belong. In the present work we do study the same phenomena for the wider Dini-Lipschitz class as well as for some other allied classes of functions.

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
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