Weighted Fourier inequalities via rearrangements
Functional Analysis
2022-01-20 v1
Abstract
The method of using rearrangements to give sufficient conditions for Fourier inequalities between weighted Lebesgue spaces is revisited. New results in the case q < p are established and a comparison between two known sufficient conditions is completed. In addition, examples are given to show that a simple weight condition that is sufficient for the weighted Fourier inequality in the cases 2 < q < p and 1 < q < p < 2 is no longer sufficient in the case 1 < q < 2 < p, contrary to statements in Theorems 1 and 4 of, "Weighted Fourier inequalities: new proofs and generalizations", J. Fourier Anal. Appl. 9 (2003), 1-37. Several alternatives are given for strengthening the simple weight condition to ensure sufficiency in that case.
Keywords
Cite
@article{arxiv.1608.02312,
title = {Weighted Fourier inequalities via rearrangements},
author = {Javad Rastegari and Gord Sinnamon},
journal= {arXiv preprint arXiv:1608.02312},
year = {2022}
}