Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation

DOI10.1016/j.aim.2006.01.010zbMath1104.46022OpenAlexW2082716720MaRDI QIDQ855517

Jie Xiao

Publication date: 7 December 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2006.01.010

zbMATH Keywords

heat equationembeddingtrace inequalityHausdorff capacityco-capacityhomogeneous endpoint Besov spaceiso-capacitary inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Heat equation (35K05) Potentials and capacities on other spaces (31C15)

Related Items (20)

A note on embedding inequalities for weighted Sobolev and Besov spaces ⋮ On fractional capacities relative to bounded open Lipschitz sets ⋮ Fractional non-linear regularity, potential and balayage ⋮ Fractional Besov trace/extension-type inequalities via the Caffarelli-Silvestre extension ⋮ Fractional Hardy-Sobolev \(L^1\)-embedding per capacity-duality ⋮ Dual characterization of fractional capacity via solution of fractional p‐Laplace equation ⋮ Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set ⋮ Capacities and embeddings of Besov spaces via general convolution kernels ⋮ Strengthened fractional Sobolev type inequalities in Besov spaces ⋮ \(L^q\)-extensions of \(L^p\)-spaces by fractional diffusion equations ⋮ The logarithmic Sobolev capacity ⋮ Optimal geometric estimates for fractional Sobolev capacities ⋮ Fractional capacities relative to bounded open Lipschitz sets complemented ⋮ Classes of Carleson-type measures generated by capacities ⋮ Carleson measure problems for parabolic Bergman spaces and homogeneous Sobolev spaces ⋮ Embeddings of function spaces via the Caffarelli-Silvestre extension, capacities and Wolff potentials ⋮ Mean Hölder-Lipschitz potentials in curved Campanato-Radon spaces and equations \((-\Delta)^{\frac{\alpha}{2}}u=\mu = F_k[u\)] ⋮ Differentiability of logarithmic Besov functions in terms of capacities ⋮ Regularity and capacity for the fractional dissipative operator ⋮ Application of capacities to space-time fractional dissipative equations. II: Carleson measure characterization for \(L^q (\mathbb{R}_+^{n+1}, \mu)\)-extension

Cites Work

• On the existence of capacitary strong type estimates in \(R^n\)
• Choquet integrals in potential theory
• Strong type estimates for homogeneous Besov capacities
• Besov functions and vanishing exponential integrability
• Some new tent spaces and duality theorems for fractional Carleson measures and \(Q_{\alpha}(\mathbb R^n)\).
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Carleson embeddings for Sobolev spaces via heat equation
• Strong type estimate and Carleson measures for Lipschitz spaces
• The co-area formula for Sobolev mappings
• Minimax Theorems
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