Weighted Geometric Mean Inequalities Over Cones in $R^N$

摘要

Let Let be a measurable subset of the unit sphere in let be a cone in and let be the part of with 'radius' A characterization of the weights and on is given such that the inequality holds for all and some positive and finite constant The inequality is obtained as a limiting case of a corresponding new Hardy type inequality. Also the corresponding companion inequalities are proved and the sharpness of the constant is discussed.