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May 2019 Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type
Hugo Aimar, Ivana Gómez
Ann. Funct. Anal. 10(2): 157-169 (May 2019). DOI: 10.1215/20088752-2018-0016

Abstract

We combine dyadic analysis through Haar-type wavelets (defined on Christ’s families of generalized cubes) and the Lax–Milgram theorem in order to prove the existence of Green’s functions for fractional Laplacians on some function spaces of vanishing small resolution in spaces of homogeneous type.

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Hugo Aimar. Ivana Gómez. "Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type." Ann. Funct. Anal. 10 (2) 157 - 169, May 2019. https://doi.org/10.1215/20088752-2018-0016

Information

Received: 28 March 2018; Accepted: 14 July 2018; Published: May 2019
First available in Project Euclid: 15 January 2019

zbMATH: 07083885
MathSciNet: MR3941378
Digital Object Identifier: 10.1215/20088752-2018-0016

Subjects:
Primary: 43A85
Secondary: 35J08 , 47N20

Keywords: energy estimates , fractional Laplacian , Haar wavelets , Sobolev Spaces , spaces of homogeneous type

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 2 • May 2019
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