A doubling subset of \(L_p\) for \(p>2\) that is inherently infinite dimensional
From MaRDI portal
Publication:464256
DOI10.1007/s10711-013-9924-4zbMath1305.30029arXiv1308.4554OpenAlexW2963683232MaRDI QIDQ464256
Publication date: 17 October 2014
Published in: Geometriae Dedicata (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1308.4554
Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Geometric embeddings of metric spaces (30L05)
Related Items (6)
The Heisenberg group associated to a Hilbert space ⋮ Vertical perimeter versus horizontal perimeter ⋮ Isometric embeddings of snowflakes into finite-dimensional Banach spaces ⋮ Embedding the Heisenberg group into a bounded-dimensional Euclidean space with optimal distortion ⋮ No dimension reduction for doubling subsets of \(\ell_q\) when \(q>2\) revisited ⋮ On the Impossibility of Dimension Reduction for Doubling Subsets of $\ell_{p}$
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces
- Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\)
- Vertical versus horizontal Poincaré inequalities on the Heisenberg group
- Cuts, trees and \(\ell_1\)-embeddings of graphs
- Assouad's theorem with dimension independent of the snowflaking
- Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
- Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
- Metric structures in \(L_1\): dimension, snowflakes, and average distortion
- Metric Characterizations of Some Classes of Banach Spaces
- Subadditivity of Homogeneous Norms on Certain Nilpotent Lie Groups
- Word distance on the discrete Heisenberg group
- On the Impossibility of Dimension Reduction for Doubling Subsets of $\ell_{p}$
- Bilipschitz embeddings of metric spaces into space forms
This page was built for publication: A doubling subset of \(L_p\) for \(p>2\) that is inherently infinite dimensional
