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)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.
Exportado de SIDERAL (2022-01-15-12:40:02)
Visitas y descargas
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)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Exportado de SIDERAL (2022-01-15-12:40:02)
Permalink:
Visitas y descargas
Este artículo se encuentra en las siguientes colecciones:
Articles > Artículos por área > Análisis Matemático
Record created 2022-01-15, last modified 2022-01-15