Absolute Continuity of Sobolev Functions and Moduli of Families of Hypersurfaces Related to Lorentz Spaces

DOI10.1007/S10958-018-3820-2zbMath1438.46042OpenAlexW2803082854WikidataQ129907393 ScholiaQ129907393MaRDI QIDQ5230726

Aleksandr Sergeevich Romanov

Publication date: 28 August 2019

Published in: Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3820-2

zbMATH Keywords

Sobolev spaceLorentz spaceabsolute continuity

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) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Cites Work

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• Extremal length and functional completion
• Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
• Weighted Hardy spaces
• Hölder quasicontinuity of Sobolev functions on metric spaces
• On functions with derivatives in a Lorentz space
• Sobolev spaces on an arbitrary metric space
• The Hölder continuity of Sobolev functions on the hypersurfaces
• The concept of capacity in the theory of functions with generalized derivatives
• The continuity of Sobolev functions on the hyperplanes

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