Norm estimates for k-plane transforms and geometric inequalities

B. Rubin

doi:10.1016/j.aim.2019.04.012

Norm estimates for k-plane transforms and geometric inequalities

B. Rubin

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	29-55
Number of pages	27
Journal	Advances in Mathematics
Volume	349
DOIs	https://doi.org/10.1016/j.aim.2019.04.012
State	Published - 20 Jun 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Geometric inequalities
Grassmann manifolds
Radon transforms

Access to Document

10.1016/j.aim.2019.04.012

Cite this

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KW - Geometric inequalities

KW - Grassmann manifolds

KW - Radon transforms

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Norm estimates for k-plane transforms and geometric inequalities

Abstract

Bibliographical note

Keywords

Access to Document

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