Almost sharp descriptions of traces of Sobolev spaces on compacta
type: Item
instance of: scholarly article
title: Almost sharp descriptions of traces of Sobolev spaces on compacta
zbMATH Open document ID: 1483.46034
DOI: 10.1134/S0001434621110377
author: Alexander Tyulenev
published in: Mathematical Notes
publication date: 2022-01-11T00:00:00Z
review text: In this short communication the author takes into account the concepts of $d$-Hausdorff measure \(H^d\), the $d$-Hausdorff content \(H^d_\infty\), dyadic Hausdorff content, and makes use of some far-reaching generalization of the Calderón maximal function. Then, as the main result a theorem is presented where the inclusions of trace spaces and the inequalities related to a suitable quotient space by the subspace of zeros of the corresponding seminorm are involved. The inclusions and the inequalities shed light on the origin of the term almost sharp description of the trace.
reviewed by: Maria Alessandra Ragusa
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7455579
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: extension operators
zbMATH Keywords: traces
zbMATH Keywords: Frostman measures
MaRDI profile type: Publication
cites work: Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
cites work: Linear extension operators for restrictions of function spaces to irregular open sets
cites work: Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝn
cites work: Sobolev \(W_p^1\)-spaces on closed subsets of \(\mathbf R^n\)
cites work: Characterization of traces of smooth functions on Ahlfors regular sets
cites work: Sobolev -spaces on -thick closed subsets of
cites work: Weakly Differentiable Functions
cites work: Traces of Sobolev functions on fractal type sets and characterization of extension domains
full work available at URL: s0001434621110377
OpenAlex ID: W4200627434
description: scientific article; zbMATH DE number 7455579