Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type

DOI10.1215/20088752-2018-0016zbMath1422.43011arXiv1803.07173OpenAlexW2789340499WikidataQ128566724 ScholiaQ128566724MaRDI QIDQ2314382

Ivana Gómez, Hugo Aimar

Publication date: 22 July 2019

Published in: Annals of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.07173

zbMATH Keywords

Sobolev spacesenergy estimatesGreen's functionsspaces of homogeneous typeDirichlet formHaar waveletsfractional LaplacianLax-Milgram theoremdyadic energyfunction spaces of coercivity

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Harmonic analysis on homogeneous spaces (43A85) Applications of operator theory to differential and integral equations (47N20) Green's functions for elliptic equations (35J08)

Cites Work

• Nonlocal Schrödinger equations in metric measure spaces
• Lipschitz functions on spaces of homogeneous type
• Multiresolution approximations and unconditional bases on weighted Lebesgue spaces on spaces of homogeneous type
• Regularity theory for parabolic nonlinear integral operators
• Extension Problem and Harnack's Inequality for Some Fractional Operators
• Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Interpolation properties of Besov spaces defined on metric spaces
• An Extension Problem Related to the Fractional Laplacian

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