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math.MG2019★ 2 cited
Ahlfors regular spaces have regular subspaces of any dimension
Nicola Arcozzi, Alessandro Monguzzi, Maura Salvatori
We characterize -dimensional Ahlfors regular spaces among trees' boundaries and show how to construct, for each , an -regular subspace. As an application, we give a…
math.CA2019
Fractional Laplacian, homogeneous Sobolev spaces and their realizations
Alessandro Monguzzi, Marco M. Peloso, Maura Salvatori
We study the fractional Laplacian and the homogeneous Sobolev spaces on R^d , by considering two definitions that are both considered classical. We compare these different definiti…