Annals of Functional Analysis

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

Hugo Aimar and Ivana Gómez

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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.

Article information

Ann. Funct. Anal., Volume 10, Number 2 (2019), 157-169.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A85: Analysis on homogeneous spaces
Secondary: 47N20: Applications to differential and integral equations 35J08: Green's functions

spaces of homogeneous type Haar wavelets energy estimates Sobolev spaces fractional Laplacian


Aimar, Hugo; Gómez, Ivana. Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type. Ann. Funct. Anal. 10 (2019), no. 2, 157--169. doi:10.1215/20088752-2018-0016.

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