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://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://openscience.fr/From-Ingham-to-Nazarov-s-inequality-a-survey-on-some-trigonometric-inequalities 
IS  - Issue 3 (June 2024) 
VL  - 15 
ER  -