We study the fractional Laplacian and the homogeneous Sobolev spaces on ℝd, by considering two defnitions that are both considered classical. We compare these diferent defnitions, 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.
Monguzzi, A., Peloso, M., Salvatori, M. (2020). Fractional Laplacian, homogeneous Sobolev spaces and their realizations. ANNALI DI MATEMATICA PURA ED APPLICATA, 199(6), 2243-2261 [10.1007/s10231-020-00966-7].
Fractional Laplacian, homogeneous Sobolev spaces and their realizations
Monguzzi, Alessandro;
2020
Abstract
We study the fractional Laplacian and the homogeneous Sobolev spaces on ℝd, by considering two defnitions that are both considered classical. We compare these diferent defnitions, 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.
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