TY - Type of reference
TI - From Ingham to Nazarov’s inequality: a survey on some trigonometric inequalities
AU - Philippe Jaming
AU - Chadi Saba
AB - The aim of this paper is to give an overview of some inequalities about $$$L^p$$$-norms ($$$p$$$ = 1 or $$$p$$$ = 2) of harmonic (periodic) and non-harmonic trigonometric polynomials. Among the material covered, we mention Ingham’s Inequality about $$$L^2$$$ norms of non-harmonic trigonometric polynmials, the proof of the Littlewood conjecture by McGehee, Pigno and Smith on the lower bound of the $$$L^1$$$ norm of harmonic trigonometric polynomials as well as its counterpart in the non-harmonic case due to Nazarov. For the later one, we give a quantitative estimate that completes our recent result with an estimate of $$$L^1$$$-norms over small intervals. We also give some stronger lower bounds when the frequencies satisfy some more restrictive conditions (lacunary Fourier series, “multi-step arithmetic sequences”). Most proofs are close to existing ones and some open questions are mentionned at the end.
DO - 10.21494/ISTE.OP.2024.1173
JF - Advances in Pure and Applied Mathematics
KW - Ingham’s Inequality, Littlewood problem, non-harmonic Fourier series, lacunary series, Ingham’s Inequality, Littlewood problem, non-harmonic Fourier series, lacunary series,
L1 - https://www.openscience.fr/IMG/pdf/iste_apam24v15n3_2.pdf
LA - en
PB - ISTE OpenScience
DA - 2024/06/12
SN - 1869-6090
TT - D’Ingham à l’inégalité de Nazarov : un survey sur quelques inégalités trigonométriques
UR - https://www.openscience.fr/From-Ingham-to-Nazarov-s-inequality-a-survey-on-some-trigonometric-inequalities
IS - Issue 3 (June 2024)
VL - 15
ER -