Norm Estimates for k-Plane Transforms and Geometric Inequalities

2017/12/30 by Rubin, Boris
#44A12 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1801.00186

Abstract

The article is devoted to remarkable interrelation between the norm estimates for k-plane transforms in weighted and unweighted L^p spaces and geometric integral inequalities for cross-sections of measurable sets in ℝⁿ. We also consider more general j-plane to k-plane transforms on affine Grassmannians and their compact modifications. The article contains a series of new integral-geometric inequalities with sharp constants, explicit equalities, conjectures, and open problems.

Related

• Weighted norm inequalities for k-plane transforms
• Results in estimates for k-plane transforms
• Uniqueness of extremizers for an endpoint inequality of the k-plane transform
• Sharp L^p-L^q estimates for generalized k-plane transforms
• Quantitative form of certain k-plane transform inequalities