On optimal autocorrelation inequalities on the real line

José Madrid, ,Department of Mathematics, University of California, Los Angeles, Portola Plaza 520, Los Angeles, California, 90095, USA, João P. G. Ramos, ,Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil
2020 Communications on Pure and Applied Analysis  
We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work [1]. In particular, we obtain improvements on the sharp constants in some of the inequalities previously considered by these authors, and also prove existence of extremizers to these inequalities in certain specific settings. Our methods consist of relating the inequalities in question to other classical sharp inequalities in Fourier analysis, such as the sharp Hausdorff-Young inequality, and employing
more » ... and employing functional analysis as well as measure theory tools in connection to a suitable dual version of the problem to identify and impose conditions on extremizers. 2020 Mathematics Subject Classification. 42A05, 42A85, 28A12, 42A82.
doi:10.3934/cpaa.2020271 fatcat:a6jxg5eehfdgvgarpzsmowrqha