Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients
Classical Analysis and ODEs
2023-10-06 v3
Abstract
We prove the Hardy-Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample, which shows that if one slightly extends the considered class of coefficients, the Hardy-Littlewood relation fails.
Keywords
Cite
@article{arxiv.2208.14405,
title = {Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients},
author = {Kristina Oganesyan},
journal= {arXiv preprint arXiv:2208.14405},
year = {2023}
}
Comments
21 pages, 1 figure. The proof of Theorem 2 was corrected