Hajłasz gradients are upper gradients

DOI10.1016/j.jmaa.2014.08.055zbMath1326.46035arXiv1307.5134OpenAlexW2964293734WikidataQ109994391 ScholiaQ109994391MaRDI QIDQ458328

Nageswari Shanmugalingam, Wen Yuan, Da Chun Yang, Ren Jin Jiang

Publication date: 7 October 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5134

zbMATH Keywords

Sobolev spacemetric measure spaceupper gradientHajłasz gradient

Mathematics Subject Classification ID

Derivatives of functions in infinite-dimensional spaces (46G05) Analysis on metric spaces (30L99)

Related Items (9)

Sobolev embeddings for fractional Hajłasz-Sobolev spaces in the setting of rearrangement invariant spaces ⋮ Extensions and approximations of Banach-valued Sobolev functions ⋮ Generalized solution of the double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces ⋮ Symmetry and compact embeddings for critical exponents in metric-measure spaces ⋮ The double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces ⋮ Maximal function estimates and self-improvement results for Poincaré inequalities ⋮ Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators ⋮ Morrey-Sobolev spaces on metric measure spaces ⋮ Gradient estimates for heat kernels and harmonic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Newtonian Lorentz metric spaces
• Nonlinear potential theory on metric spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Lectures on analysis on metric 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
• Variable exponent Sobolev spaces on metric measure spaces
• Morrey-Sobolev spaces on metric measure spaces
• Pointwise characterizations of Hardy-Sobolev functions
• Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices
• Morrey Spaces on Spaces of Homogeneous Type and Estimates for □_b and the Cauchy‐Szegö Projection
• Sobolev met Poincaré
• Extension of range of functions

This page was built for publication: Hajłasz gradients are upper gradients