\(L^q\)-extensions of \(L^p\)-spaces by fractional diffusion equations

DOI10.3934/dcds.2015.35.1905zbMath1303.31007OpenAlexW2316625548MaRDI QIDQ484414

Jie Xiao, Der-Chen E. Chang

Publication date: 7 January 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.1905

zbMATH Keywords

heat kernelfractional diffusion equations\(L^p\)-type capacities\(L^q\)-extensions

Mathematics Subject Classification ID

Potentials and capacities on other spaces (31C15) Heat kernel (35K08)

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A capacity associated with the weighted Lebesgue space and its applications ⋮ 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 ⋮ Toward weighted Lorentz-Sobolev capacities from Caffarelli-Silvestre extensions ⋮ A tracing of the fractional temperature field ⋮ Fractional heat semigroups on metric measure spaces with finite densities and applications to fractional dissipative equations ⋮ Embeddings of function spaces via the Caffarelli-Silvestre extension, capacities and Wolff potentials ⋮ 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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