A density result for homogeneous Sobolev spaces

Nandi, Debanjan

doi:10.1016/j.na.2021.112501

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Homogeneous versions of Newton-Sobolev spaces, where the energy of the function in that version is globally finite without the function itself being necessarily in the global L pclass, arise naturally when dealing with large-scale potential theory of a metric measure space; see for example [4,10,11,18,1]. For this reason, the behavior of such functions has attracted great interest recently, and an interesting discussion about limits at infinity of such functions can be found in the metric space context in [15,14,3,13].…”

Section: Introductionmentioning

confidence: 99%

A Universality Property of Sobolev Spaces in Metric Measure Spaces

Shanmugalingam

International Mathematical Series

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In this note we prove the Banach space properties of the homogeneous Newton-Sobolev spaces HN 1,p (X) of functions on an unbounded metric measure space X equipped with a doubling measure supporting a p-Poincaré inequality, and show that when 1 < p < ∞, even with the lack of global L p -integrability of functions in HN 1,p (X), we have that every bounded sequence in HN 1,p (X) has a strongly convergent convex-combination subsequence. The analogous properties for the inhomogeneous Newton-Sobolev classes N 1,p (X) are proven elsewhere in existing literature (as for example in [19,9]).

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Section: Introductionmentioning

confidence: 99%

A Universality Property of Sobolev Spaces in Metric Measure Spaces

Shanmugalingam

International Mathematical Series

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Gromov hyperbolicity and unbounded uniform domains

Zhou,

He,

Rasila

et al. 2024

manuscripta math.

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Geometric characterizations of Gromov hyperbolic Hölder domains

Zhou

Rasila

2022

Forum Mathematicum

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In this paper, we investigate Hölder continuity of quasiconformal mappings in ℝ n {\mathbb{R}^{n}} from the points of view of quasihyperbolic geometry and the theory of Gromov hyperbolic spaces. We establish several characterizations of Gromov hyperbolic domains satisfying the Gehring–Martio-type quasihyperbolic boundary conditions. As applications, we generalize certain results concerning Hölder continuity of conformal mappings, establishing counterparts of results of Becker and Pommerenke, Smith and Stegenga, and Näkki and Palka in higher-dimensional Euclidean spaces.

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A density result for homogeneous Sobolev spaces

Cited by 3 publications

References 13 publications

A Universality Property of Sobolev Spaces in Metric Measure Spaces

A Universality Property of Sobolev Spaces in Metric Measure Spaces

Gromov hyperbolicity and unbounded uniform domains

Geometric characterizations of Gromov hyperbolic Hölder domains

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