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Absolute convergence factors of Lipschitz class functions for general Fourier series. (English) Zbl 1492.42001

Summary: The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions \(f\in\operatorname{Lip}1\) class provides absolute convergence of Fourier series. In particular, we found special conditions for the functions of orthonormal system (ONS), for which the above sequences are absolute convergence factors of Fourier series of functions of \(\operatorname{Lip}1\) class. It is established that the resulting conditions are best possible in certain sense.

MSC:

42A20 Convergence and absolute convergence of Fourier and trigonometric series
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
46B07 Local theory of Banach spaces
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References:

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