Norm estimates for k-plane transforms and geometric inequalities

被引：4
|
作者：
Rubin, B. [1 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
来源：
ADVANCES IN MATHEMATICS | 2019年 / 349卷
关键词：
Radon transforms; Grassmann manifolds; Geometric inequalities; DUAL AFFINE QUERMASSINTEGRALS; RADON TRANSFORMS; MAPPING PROPERTIES; FURSTENBERG; SECTIONS; BUSEMANN; VALUATIONS; INVERSION; INTEGRALS; CONSTANT;
D O I：
10.1016/j.aim.2019.04.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 R-n. A similar interrelation is studied for 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. (C) 2019 Elsevier Inc. All rights reserved.
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页码：29 / 55
页数：27
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