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Article · Studia Mathematica · August 6, 2019

Hardy–Littlewood theorems for trigonometric series with general monotone coefficients

Mikhail Ivanovich Dyachenko, Askhat Birlesovich Mukanov, Sergey Yu. Tikhonov

Askhat Mukanov
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Abstract

We study trigonometric series with general monotone coefficients, i.e., satisfying $$ \sum _{k=n}^{2n}|a_k - a_{k+1}| \le {C} \sum _{k = {n/\lambda }}^{\lambda n}\frac {|a_k|}{k} , \hskip 1em n \in \mathbb {N}, $$ for some $C \gt 0$ and $\lambda \gt 1$. F

Advanced Harmonic Analysis ResearchApproximation Theory and Sequence SpacesMathematical Analysis and Transform MethodsHardy-Littlewood theoremtrigonometric seriesmonotone coefficients

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