Monotone extremal functions and the weighted Hilbert's inequality
Classical Analysis and ODEs
2023-07-04 v2 Number Theory
Abstract
In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the (non-sharp) weighted Hilbert-Montgomery-Vaughan inequality.
Keywords
Cite
@article{arxiv.2302.14658,
title = {Monotone extremal functions and the weighted Hilbert's inequality},
author = {Emanuel Carneiro and Friedrich Littmann},
journal= {arXiv preprint arXiv:2302.14658},
year = {2023}
}
Comments
7 pages, 3 figures. To appear in Portugaliae Mathematica