Collection Shapes and shades of Analysis: in depth and beyond / Formes et nuances de l'analyse moderne

Organizer(s) Abakumov, Evgeny ; Charpentier, Stéphane ; Kupin, Stanislas ; Tomilov, Yuri ; Zarouf, Rachid

Date(s) 29/04/2024 - 03/05/2024

linked URL https://conferences.cirm-math.fr/3004.html

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Schatten class of Sobolev embeddings, and how fast can/must oscillate an $L^2$ basis

The "positivity phenomenon" for Bessel sequences, frames and Riesz bases $\left(u_k\right)$ are studied in $L^2$ spaces over the compacts of homogeneous (Coifman-Weiss) type $\Omega=(\Omega, \rho, \mu)$. Under some relations between three basic metric-measure dimensions of $\Omega$, we obtain asymptotics for the mass moving norms $\left|u_k\right|_{K R}$ (Kantorovich-Rubinstein), as well as for singular numbers of the Lipschitz and Hajlasz-Sobolev embeddings. Our main observation shows that, quantitatively, the rate of the convergence $\left|u_k\right|_{K R} \longrightarrow 0$ depends on an interplay between geometric doubling and measure doubling/halving exponents. The "more homogeneous" is the space, the sharper are the results.

Information about the video

Date of recording 29/04/2024
Date of publication 24/05/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20168503
Cite this video Nikolski, Nikolaï (29/04/2024). Schatten class of Sobolev embeddings, and how fast can/must oscillate an $L^2$ basis. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20168503
URL https://dx.doi.org/10.24350/CIRM.V.20168503

Domain(s)

Classical Analysis and ODEs

Bibliography

NIKOLSKI, N. Three dimensions of metric-measure spaces, Sobolev embeddings and optimal sign transport. St. Petersburg Mathematical Journal, 2023, vol. 34, no 2, p. 221-245. - https://doi.org/10.1090/spmj/1752