On concentration, deviation and Dvoretzky's theorem for Besov, Lizorkin–Triebel and other spaces

DOI10.1080/17476930903394739zbMath1214.46007OpenAlexW1968205773MaRDI QIDQ4931828

Sergey Ajiev

Publication date: 1 October 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930903394739

zbMATH Keywords

Sobolev spacesBesov spacesLizorkin-Triebel spacesDvoretzky's theoremconcentration of measure and distanceindependently generated space

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) Local theory of Banach spaces (46B07) Classical Banach spaces in the general theory (46B25) Probabilistic methods in Banach space theory (46B09) Banach sequence spaces (46B45)

Related Items (1)

Quantitative Hahn-Banach theorems and isometric extensions for wavelet and other Banach spaces

Cites Work

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• Two observations regarding embedding subsets of Euclidean spaces in normed spaces
• Some inequalities for Gaussian processes and applications
• Some deviation inequalities
• The Brunn-Minkowski inequality in Gauss space
• The dimension of almost spherical sections of convex bodies
• From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
• Comparison of moments of sums of independent random variables and differential inequalities
• A measure concentration inequality for contracting Markov chains
• Symétrisation dans l'espace de Gauss.
• Concentration of the distance in finite dimensional normed spaces

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