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.

Fractional Laplacian, homogeneous Sobolev spaces and their realizations / A. Monguzzi, M.M. Peloso, M. Salvatori. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2020). [Epub ahead of print]

Fractional Laplacian, homogeneous Sobolev spaces and their realizations

M.M. Peloso
Secondo
;
M. Salvatori
Ultimo
2020

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.
Homogeneous Sobolev spaces; Fractional Laplacian
Settore MAT/05 - Analisi Matematica
   Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   2015A35N9B_007
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/718966
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