A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces

DOI10.54330/AFM.127419OpenAlexW4322722545MaRDI QIDQ5883044

Ryan Alvarado, Lukáš Malý, Piotr Hajłasz

Publication date: 29 March 2023

Published in: Annales Fennici Mathematici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.13932

zbMATH Keywords

Sobolev spacesPoincaré inequalityuniform convexityanalysis on metric spaces

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Potential theory on fractals and metric spaces (31E05) Analysis on metric spaces (30L99) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear potential theory on metric spaces
• An elementary proof of Cheeger's theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Definitions of Sobolev classes on metric spaces
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces on an arbitrary metric space
• The Poincaré inequality is an open ended condition
• Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
• Nonsmooth calculus
• Alternative proof of Keith–Zhong self-improvement and connectivity
• Sobolev Spaces on Metric Measure Spaces
• Uniformly Convex Spaces

This page was built for publication: A simple proof of reflexivity and separability of N^{1,p} Sobolev spaces