Orlicz-log宽度积分的Orlicz-Brunn-Minowski型不等式

ORLICZ-BRUNN-MINKOWSKI TYPE INEQUALITIES OF ORLICZ-LOG WIDTH INTEGRALS

本文基于Brunn-Minkowski理论中宽度积分的研究,定义了Orlicz-log宽度积分,建立Orlicz-log宽度积分的Orlicz-Minkowski型不等式和Orlicz-Brunn-Minowski型不等式及它们间的等价关系。当φ(x,y)=x^(-p)+y^(-p)时,即为L_(p)-log宽度积分的Lp-Minkowski型不等式和L_(p)-Brunn-Minowski型不等式。

Based on the study of width integral in Brunn-Minkowski theory,we define the Orlicz-log width integral and establish the Orlicz-Minowski type inequality and the Orlicz-Brunn-Minkowski type inequality of the Orlicz-log width integral as well as their equivalence relationship.Whenφ(x,y)=x^(-p)+y^(-p)is satisfied,the inequalities of Orlicz-log width integral is correspondingly transformed to L_(p)-Minowski type inequality and L_(p)-Brunn-Minkowski type inequality of L_(p)-log width integral.