Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (1): 52-71.doi: 10.1007/s10473-025-0105-y

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A FUNCTIONAL ORLICZ BUSEMANN-PETTY CENTROID INEQUALITY FOR LOG-CONCAVE FUNCTIONS

Xiao Li1, Jiazu Zhou2,*   

  1. 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;
    2. School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China
  • Received:2024-08-01 Published:2025-02-06
  • Contact: *Jiazu Zhou, E-mail,: zhoujz@gznc.edu.cn; zhoujz@swu.edu.cn
  • About author:Xiao Li, E-mail,: lxlixiaolx@163.com
  • Supported by:
    NSFC(12071378, 12461009),20XLB012, KJQN202100527, CSTB2022NSCQ-MSX0259 and KJQN202300557.

Abstract: In this paper, the Orlicz centroid function for log-concave functions is introduced. A rearrangement inequality of the Orlicz centroid function for log-concave functions is obtained. The rearrangement inequality implies the Orlicz Busemann-Petty centroid inequality of Lutwak, Yang and Zhang [23].

Key words: centroid bodies, Busemann-Petty centroid inequality, log-concave functions, Steiner symmetrization

CLC Number: 

  • 52A40
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