Geodesic
Piecewise General Monotone Functions and the Hardy--Littlewood Theorem
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 120-133.

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We obtain necessary and sufficient conditions for an integrable piecewise general monotone function to belong to an $L^p$ space with a weight of Muckenhoupt class $\mathbb A_p$ 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. 
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M. I. Dyachenko; S. Yu. Tikhonov. Piecewise General Monotone Functions and the Hardy--Littlewood Theorem. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 120-133. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a9/

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