Abstract
Extending the notion of the general monotonicity for sequences to functions, we exploit it to investigate integrability problems for Fourier transforms. The problem of controlling integrability properties of the Fourier transform separately near the origin and near infinity is examined. We then apply the obtained results to the problems of integrability of trigonometric series.
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Liflyand, E., Tikhonov, S. (2009). The Fourier Transforms of General Monotone Functions. In: Gustafsson, B., Vasil’ev, A. (eds) Analysis and Mathematical Physics. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9906-1_18
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DOI: https://doi.org/10.1007/978-3-7643-9906-1_18
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