Embeddings of function spaces via the Caffarelli-Silvestre extension, capacities and Wolff potentials

DOI10.1016/j.na.2021.112758zbMath1483.35077arXiv2007.00713OpenAlexW3040050238MaRDI QIDQ2074927

Zhichun Zhai, Rui Hu, Shaoguang Shi, Pengtao Li

Publication date: 11 February 2022

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/2007.00713

zbMATH Keywords

Sobolev spaceLebesgue spacecapacityfractional Laplacian

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractional partial differential equations (35R11)

Related Items

Fractional Besov trace/extension-type inequalities via the Caffarelli-Silvestre extension ⋮ Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set ⋮ BV capacity and perimeter in abstract Wiener spaces and applications ⋮ Capacities and embeddings of Besov spaces via general convolution kernels ⋮ Strengthened fractional Sobolev type inequalities in Besov spaces ⋮ Toward weighted Lorentz-Sobolev capacities from Caffarelli-Silvestre extensions ⋮ Application of capacities to space-time fractional dissipative equations. II: Carleson measure characterization for \(L^q (\mathbb{R}_+^{n+1}, \mu)\)-extension

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