Nonmultipliers of the Sobolev spaces \(W^{k,1}({\mathbb{R}}^ n)\)

DOI10.1016/0022-1236(87)90021-8zbMath0627.46034OpenAlexW2040576748MaRDI QIDQ1092373

S. Poornima, Aline Bonami

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0022-1236(87)90021-8

zbMATH Keywords

tempered distributionsingular integral operatorsFourier multiplierhomogeneous Sobolev space

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) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Multipliers for harmonic analysis in several variables (42B15)

Related Items (8)

On rank one convex functions that are homogeneous of degree one ⋮ On the continuity of Fourier multipliers on \(\dot{W}^{l,1}(\mathbb{R}^d)\) and \(\dot{W}^{l,\infty}(\mathbb{R}^d)\) ⋮ On the continuity of Fourier multipliers on the homogeneous Sobolev spaces \(\dot{W}_1^1(R^d)\) ⋮ Fourier Multipliers of the Homogeneous Sobolev Space Ẇ 1,1 ⋮ A noninequality for the fractional gradient ⋮ An optimal Sobolev embedding for \(L^1\) ⋮ Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori ⋮ Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group

Cites Work

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• A non-inequality for differential operators in the \(L_ 1\) norm
• Multipliers of Sobolev spaces
• Les espaces du type de Beppo Levi

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