We study the fractional Laplacian and the homogeneous Sobolev spaces on Rd, by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way, we also prove some properties of the fractional Laplacian.
(2020). Fractional Laplacian, homogeneous Sobolev spaces and their realizations [journal article - articolo]. In ANNALI DI MATEMATICA PURA ED APPLICATA. Retrieved from http://hdl.handle.net/10446/202834
Fractional Laplacian, homogeneous Sobolev spaces and their realizations
Monguzzi, Alessandro;
2020-01-01
Abstract
We study the fractional Laplacian and the homogeneous Sobolev spaces on Rd, by considering two definitions that are both considered classical. We compare these different definitions, and show how they are related by providing an explicit correspondence between these two spaces, and show that they admit the same representation. Along the way, we also prove some properties of the fractional Laplacian.File allegato/i alla scheda:
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