Some Inequalities for Multiple Integrals on the n -Dimensional Ellipsoid, Spherical Shell, and Ball

Abstract

The authors establish some new inequalities of Pólya type for multiple integrals on the $n$-dimensional ellipsoid, spherical shell, and ball, in terms of bounds of the higher order derivatives of the integrands. These results generalize the main result in the paper by Feng Qi, Inequalities for a multiple integral, Acta Mathematica Hungarica (1999).