Regularity Properties of Commutators and Layer Potentials Associated to the Heat Equation

DOI10.2307/2001805zbMath0780.35049OpenAlexW4247524577MaRDI QIDQ3984304

Margaret A. M. Murray, John L. Lewis

Publication date: 27 June 1992

Full work available at URL: https://doi.org/10.2307/2001805

zbMATH Keywords

regularityheat equationBMOcommutator estimatesparabolic boundary value problemsboundary single layer potential

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximal functions, Littlewood-Paley theory (42B25) Initial-boundary value problems for second-order parabolic equations (35K20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Commutators, derivations, elementary operators, etc. (47B47) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (9)

Harmonic measure and heat equation ⋮ Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials ⋮ Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition ⋮ Commutators with fractional differentiation for second-order elliptic operators on ℝn ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates ⋮ A Note on Weighted Sobolev Spaces, and Regularity of Commutators and Layer Potentials Associated to the Heat Equation ⋮ Commutators of square functions related to fractional differentiation for second-order elliptic operators ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators ⋮ Necessary and sufficient conditions for the bounds of the commutators with fractional differentiations and BMO-Sobolev spaces on weighted Lebesgue space

Cites Work

• A boundedness criterion for generalized Calderón-Zygmund operators
• The Initial-Neumann Problem for the Heat Equation in Lipschitz Cylinders
• The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders
• Multilinear singular integrals involving a derivative of fractional order
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