Fourier transform is an isometry on some weighted Sobolev spaces

DOI10.1016/j.matpur.2012.09.010zbMath1281.42008OpenAlexW2092422582MaRDI QIDQ387852

Tahar Zamène Boulmezaoud

Publication date: 17 December 2013

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2012.09.010

zbMATH Keywords

Fourier transformweighted Sobolev spaceisometryinvariant spacePlancherel identity

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Cites Work

• Theory of Bessel potentials. I
• Elliptic systems in H(s,delta) spaces on manifolds which are Euclidean at infinity
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• On the invariance of weighted Sobolev spaces under Fourier transform
• Weighted \(L^p\) theory of the Stokes and the bilaplacian operators in the half-space
• On the steady Oseen problem in the whole space
• On spaces of potentials connected with \(L^ p\) classes
• On the Laplace operator and on the vector potential problems in the half‐space: an approach using weighted spaces
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