Sobolev-Lorentz spaces in the Euclidean setting and counterexamples

DOI10.1016/j.na.2017.01.001zbMath1366.31005arXiv1605.08551OpenAlexW2400069141WikidataQ124812491 ScholiaQ124812491MaRDI QIDQ511417

Şerban Costea

Publication date: 15 February 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08551

zbMATH Keywords

embedding theoremsLorentz spacesSobolev-Lorentz spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Other generalizations (nonlinear potential theory, etc.) (31C45)

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Cites Work

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• Newtonian Lorentz metric spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Lectures on analysis on metric spaces
• On functions with derivatives in a Lorentz space
• Definitions of Sobolev classes on metric spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Boundary continuity for quasiminimizers on metric spaces
• Sobolev spaces on an arbitrary metric space
• Change of variables for absolutely continuous functions
• On L(p,q) spaces
• Fine behavior of functions whose gradients are in an Orlicz space
• Conductor Inequalities and Criteria for Sobolev-Lorentz Two-Weight Inequalities
• Scaling invariant Sobolev-Lorentz capacity on $\mathbb{R}^{n}$
• Harmonic functions on metric spaces