Some conjectures aboutLp norms of k-plane transforms

DOI10.1007/BF02930488zbMath1016.44002OpenAlexW2000295065WikidataQ123009251 ScholiaQ123009251MaRDI QIDQ4802646

Albert II Baernstein, Michael Loss

Publication date: 22 April 2003

Published in: Rendiconti del Seminario Matematico e Fisico di Milano (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02930488

zbMATH Keywords

Radon transformextremal function\(L^{p}\)-norm\(k\)-plane transform

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Radon transform (44A12) Length, area, volume, other geometric measure theory (28A75)

Related Items (9)

Norm estimates for \(k\)-plane transforms and geometric inequalities ⋮ A probabilistic take on isoperimetric-type inequalities ⋮ A multilinear generalisation of the Hilbert transform and fractional integration ⋮ A convex body associated to the Busemann random simplex inequality and the Petty conjecture ⋮ Volume of the polar of random sets and shadow systems ⋮ Bounding marginal densities via affine isoperimetry ⋮ A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury's identity ⋮ Quantitative form of certain \(k\)-plane transform inequalities ⋮ Uniqueness of extremizers for an endpoint inequality of the \(k\)-plane transform

Cites Work

• Maximum and minimum sets for some geometric mean values
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Generalizations of Riesz potentials and \(L^ p\) estimates for certain k- plane transforms
• Extremals of functionals with competing symmetries
• \(L^p\) estimates for the X-ray transform
• Best constant in Sobolev inequality
• A general rearrangement inequality for multiple integrals
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• A Note on Some Inequalities
• Isotropic random simplices
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