Hugo Aimar, Ivana Gómez. Source: Annals of Functional Analysis, Advance publication, 13 pages.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.