doi:10.1016/j.jmaa.2020.123875engAlonso Gutiérrez, DavidBernués, JulioGonzález Merino, BernardoAn extension of Berwald's inequality and its relation to Zhang's inequalityART-2020-116023In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function f:Rn→[0, ∞)and any concave function h :L →[0, ∞), where L ={(x, t) ∈Rn×[0, ∞) :f(x) ≥e−t‖f‖∞}, then p→⎛⎝1Γ(1 +p)∫Le−tdtdx∫Lhp(x, t)e−tdtdx⎞⎠1p is decreasing in p ∈(−1, ∞), extending the range of pwhere the monotonicity is known to hold true.As an application of this extension, we will provide a new proof of a functional form of Zhang’s reverse Petty projection inequality, recently obtained in [2].2020http://zaguan.unizar.es/record/10944410.1016/j.jmaa.2020.123875http://zaguan.unizar.es/record/109444oai:zaguan.unizar.es:109444Journal of Mathematical Analysis and Applications 486, 1 (2020), 123875 1-10by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess