Piecewise General Monotone Functions and the Hardy–Littlewood Theorem

We obtain necessary and sufficient conditions for an integrable piecewise general monotone function to belong to an space with a weight of Muckenhoupt class in terms of the Fourier coefficients. We also find a sufficient condition for the Hardy transform of an arbitrary integrable function to belong...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2022-12, Vol.319 (1), p.110-123
Main Authors: Dyachenko, M. I., Tikhonov, S. Yu
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Mathematics
Mathematics and Statistics
Monotone functions
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Summary:We obtain necessary and sufficient conditions for an integrable piecewise general monotone function to belong to an space with a weight of Muckenhoupt class in terms of the Fourier coefficients. We also find a sufficient condition for the Hardy transform of an arbitrary integrable function to belong to the same space.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543822050108