Banach spaces of functions and distributions characterized by singular integrals involving the Fourier transform

DOI10.1016/0022-1236(92)90043-IzbMath0774.46024OpenAlexW2086571153MaRDI QIDQ1803331

Rodney Nillsen

Publication date: 29 June 1993

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90043-i

zbMATH Keywords

Fourier transformsspace of tempered distributionsinvariant formsgeneralized differencesSobolev-type space determined by integrals, rather than derivatives

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integral transforms in distribution spaces (46F12) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (4)

Differences of functions and group generators for compact Abelian groups ⋮ Sharpness results concerning finite differences in Fourier analysis on the circle group ⋮ Vanishing Fourier Transforms and Generalized Differences in ⋮ Vanishing Fourier coefficients and the expression of functions in \(L^2(\mathbb{T})\) as sums of generalised differences

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Translation invariant forms on \(L^ p(G)\) \((1<p<\infty)\)
• Diophantine approximation
• Translation-invariant linear forms on C\(_0\)(G), C(G), L\(^p\)(G) for noncompact groups
• Translationinvariant linear forms on L\(^2\)(G) for compact Abelian groups G
• Some discontinuous translation-invariant linear forms
• Adapted Sets of Measures and Invariant Functionals on L p (G)

This page was built for publication: Banach spaces of functions and distributions characterized by singular integrals involving the Fourier transform