Fractional Laplacian, homogeneous Sobolev spaces and their realizations

DOI10.1007/s10231-020-00966-7zbMath1473.46043arXiv1910.05980OpenAlexW3009578234MaRDI QIDQ2210726

Marco M. Peloso, Alessandro Monguzzi, Maura Salvatori

Publication date: 8 November 2020

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.05980

zbMATH Keywords

fractional Laplacianhomogeneous Sobolev spaces

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (8)

Fractional Paley-Wiener and Bernstein spaces ⋮ Homogeneous algebras via heat kernel estimates ⋮ Characterisation of homogeneous fractional Sobolev spaces ⋮ Rectification of a deep water model for surface gravity waves ⋮ Sobolev algebras on Lie groups and noncommutative geometry ⋮ Sharp approximation theorems and Fourier inequalities in the Dunkl setting ⋮ Sampling in spaces of entire functions of exponential type in \(\mathbb{C}^{n + 1} \) ⋮ Periodic Hölder waves in a class of negative-order dispersive equations

Cites Work

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• Hitchhiker's guide to the fractional Sobolev spaces
• Tempered homogeneous function spaces
• Ten equivalent definitions of the fractional Laplace operator
• Lipschitz spaces, smoothness of functions, and approximation theory
• Réalisations des espaces de Besov homogènes. (Realization of homogeneous Besov spaces)
• A note on Riesz potentials
• Sobolev spaces on Lie groups: embedding theorems and algebra properties
• Sobolev algebras on nonunimodular Lie groups
• A density result for homogeneous Sobolev spaces on planar domains
• Besov and Triebel-Lizorkin spaces on Lie groups
• A note on homogeneous Sobolev spaces of fractional order
• A complete real-variable theory of Hardy spaces on spaces of homogeneous type
• Realizations of homogeneous Sobolev spaces
• Tempered homogeneous function spaces, II
• Fractional integration on Hardy spaces
• Realizations of homogeneous Besov and Lizorkin‐Triebel spaces
• Classical Fourier Analysis
• Modern Fourier Analysis
• An Extension Problem Related to the Fractional Laplacian
• Fractional powers of operators

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