PreprintCC BY 4.0arXiv
Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains
Abstract
For any convex set Ω⊂ℝn that does not contain affine lines, we prove the inequality ∫Ω|f̂(x)|2/ωΩ(x) dx≤ C(n)|f|L12, suppf̂⊂Ω, where ωΩ(x)=m(Ω∩(2x−Ω)). As a consequence, we derive a weak factorization for PW1(Ω)={f∈ L1(ℝn):suppf̂⊂Ω}. Furthermore, we establish a complete characterization of Schatten class Hankel operators for polyhedra for all 1≤ p<∞, extending the already known 1≤ p≤ 2 range.
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BibTeX
@misc{bampouras2026helson,
title = {{Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains}},
author = {Konstantinos Bampouras},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10730},
eprint = {2609.10730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10730},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains
AU - Konstantinos Bampouras
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10730
UR - https://arxiv.org/abs/2609.10730
AB - For any convex set Ω⊂ℝ^n that does not contain affine lines, we prove the inequality ∫_Ω|f̂(x)|^2/ω_Ω(x) dx≤ C(n)|f|_L^1^2, suppf̂⊂Ω, where ω_Ω(x)=m(Ω∩(2x−Ω)). As a consequence, we derive a weak factorization for PW^1(Ω)={f∈ L^1(ℝ^n):suppf̂⊂Ω}. Furthermore, we establish a complete characterization of Schatten class Hankel operators for polyhedra for all 1≤ p<∞, extending the already known 1≤ p≤ 2 range.
ER -