TY - Type of reference TI - [FORTHCOMING] D’Ingham à l’inégalité de Nazarov : un survey sur quelques inégalités trigonométriques 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 - À venir JF - Avancées en Mathématiques Pures et Appliquées KW - Ingham’s Inequality, Littlewood problem, non-harmonic Fourier series, lacunary series, Ingham’s Inequality, Littlewood problem, non-harmonic Fourier series, lacunary series, L1 - LA - fr PB - ISTE OpenScience DA - 2024/03/15 SN - 1869-6090 TT - [FORTHCOMING] From Ingham to Nazarov’s inequality: a survey on some trigonometric inequalities UR - http://openscience.fr/D-Ingham-a-l-inegalite-de-Nazarov-un-survey-sur-quelques-inegalites IS - Articles à paraître
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