On strict inclusions in hierarchies of convex bodies

DOI10.1090/S0002-9939-08-09424-0zbMath1149.52005arXiv0707.1471OpenAlexW2110601059MaRDI QIDQ3522329

Vladyslav Yaskin

Publication date: 1 September 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1471

zbMATH Keywords

isometric embeddingradial functionintersection bodystar body\(L_p\)-spaces\(k\)-intersection bodyradial metric

Mathematics Subject Classification ID

Isometric theory of Banach spaces (46B04) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (9)

Projection functions, area measures and the Alesker-Fourier transform ⋮ Inequalities for the derivatives of the Radon transform on convex bodies ⋮ On convex intersection bodies and unique determination problems for convex bodies ⋮ On sections of convex bodies in hyperbolic space ⋮ Counterexamples to convexity of $k$-intersection bodies ⋮ Intersection bodies and generalized cosine transforms ⋮ Isomorphic properties of intersection bodies ⋮ Positive definite distributions and normed spaces ⋮ Slicing inequalities for subspaces of $L_p$

Cites Work

• Unnamed Item
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• Generalized intersection bodies
• Representation of \(L_ p\)-norms and isometric embedding in \(L_ p\)- spaces
• Intersection bodies and dual mixed volumes
• Zonoide und verwandte Klassen konvexer Körper
• Spherical projections and centrally symmetric sets
• Generalized intersection bodies are not equivalent
• Non-intersection bodies, all of whose central sections are intersection bodies
• A note on 𝑘-intersection bodies
• Positive Definite Distributions and Subspaces of L__p With Applications to Stable Processes
• Banach spaces embedding isometrically into $L{\textunderscore }p$ when $0<p<1$
• A Banach subspace of 𝐿_{1/2} which does not embed in 𝐿₁ (isometric version)
• Sections of Convex Bodies
• A functional analytic approach to intersection bodies

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