Some Brunn-Minkowski type inequalities for L p $L_{p}$ radial Blaschke-Minkowski homomorphisms

Abstract

Abstract Schuster introduced radial Blaschke-Minkowski homomorphisms. Recently, they were generalized to L p $L_{p}$ radial Blaschke-Minkowski homomorphisms by Wang et al. In this paper, we first establish Brunn-Minkowski type inequalities for some L q $L_{q}$ radial sums of L p $L_{p}$ radial Blaschke-Minkowski homomorphisms. Further, we consider monotonic inequalities for L p $L_{p}$ radial Blaschke-Minkowski homomorphisms.

Keywords

• L p $L_{p}$ radial Blaschke-Minkowski homomorphism
• Brunn-Minkowski inequality
• L q $L_{q}$ radial sum
• monotonic inequality