Hardy-type theorems on Fourier transforms revised

We obtain new conditions on periodic integrable functions so that their transformed Fourier series belong to Lp. This improves the classical Hardy and Bellman results. A counterpart for the Fourier transforms is also established. Our main tool is a new extension of the Hausdorff–Young–Paley inequali...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-11, Vol.467 (1), p.171-184
Main Authors: Dyachenko, M., Nursultanov, E., Tikhonov, S.
Format: Article
Language:English
Subjects:
Fourier coefficients/transforms
Hardy and Hardy–Cesàro averages
Hardy–Littlewood theorem
Hausdorff–Young–Paley inequality
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Summary:We obtain new conditions on periodic integrable functions so that their transformed Fourier series belong to Lp. This improves the classical Hardy and Bellman results. A counterpart for the Fourier transforms is also established. Our main tool is a new extension of the Hausdorff–Young–Paley inequality for Fourier transforms.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.06.072