Hardy–Littlewood theorems for trigonometric series with general monotone coefficients
Volume 250 / 2020
Studia Mathematica 250 (2020), 217-234
MSC: Primary 26A48, 42A16, 42A32, 46E30.
DOI: 10.4064/sm180225-13-10
Published online: 6 August 2019
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 $\lambda \gt 1$. For such series we prove Hardy–Littlewood-type theorems for Lorentz and weighted Lebesgue spaces.
