Document Type
Article
Publication Date
6-20-2019
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 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.
Publication Source (Journal or Book title)
Advances in Mathematics
First Page
29
Last Page
55
Recommended Citation
Rubin, B. (2019). Norm estimates for k-plane transforms and geometric inequalities. Advances in Mathematics, 349, 29-55. https://doi.org/10.1016/j.aim.2019.04.012
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