Sharp norm estimates for functional dual affine quermassintegrals

This paper presents refined estimates for functional dual affine quermassintegrals, building upon the estimates of Dann et al. To sharpen the inequality, Dann et al. (Proc. Lond. Math. Soc. (3) 113(2):140–162, 2016) incorporated an \(L^\infty\) $L^{\infty }$ -weight into the integration. We further refine these estimates and extend the \(L^\infty\) $L^{\infty }$ -weight estimates to include a wider range of \(L^{\lambda }\) $L^{\lambda }$ -weights where \(\lambda >1.\) $\lambda >1.$