An extension of Berwald's inequality and its relation to Zhang's inequality

Alonso Gutiérrez, David (Universidad de Zaragoza) ; Bernués, Julio (Universidad de Zaragoza) ; González Merino, Bernardo

Resumen: In 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].

Idioma: Inglés

DOI: 10.1016/j.jmaa.2020.123875

Año: 2020

Publicado en: Journal of Mathematical Analysis and Applications 486, 1 (2020), 123875 1-10
ISSN: 0022-247X

Factor impacto JCR: 1.583 (2020)

Categ. JCR: MATHEMATICS rank: 63 / 330 = 0.191 (2020) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 109 / 265 = 0.411 (2020) - Q2 - T2

Factor impacto SCIMAGO: 0.95 - Applied Mathematics (Q1) - Analysis (Q1)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)