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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1547542826

Digital Object Identifier
doi:10.1215/20088752-2018-0016

Mathematical Reviews number (MathSciNet)
MR3941378

Zentralblatt MATH identifier
07083885

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

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

Citation

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. https://projecteuclid.org/euclid.afa/1547542826


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References

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