Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms

DOI10.1090/memo/1230zbMath1445.42001arXiv1511.05702OpenAlexW2963129766WikidataQ129202818 ScholiaQ129202818MaRDI QIDQ5383904

Alexander Nagel, Fulvio Ricci, Stephen Wainger, Elias M. Stein

Publication date: 20 June 2019

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.05702

zbMATH Keywords

singular integral operatorsflag kernelspseudo-differential operatorsmultiplier operatorsmulti-parameter theoryhomogeneous nilpotent Lie groups

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Integral operators (47G10) Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces (42-02)

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Cites Work

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• Characterizations of multiparameter Besov and Triebel-Lizorkin spaces associated with flag singular integrals
• Singular integrals with flag kernels on homogeneous groups, I
• An atomic decomposition characterization of flag Hardy spaces \(H^p_F(\mathbb R^n\times\mathbb R^m)\) with applications
• Weighted norm inequalities for flag singular integrals on homogeneous groups
• Non-isotropic flag singular integrals on multi-parameter Hardy spaces
• Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals
• Weighted Hardy spaces in the three-parameter case
• Besov and Triebel-Lizorkin spaces related to singular integrals with flag kernels
• Harmonic analysis on nilpotent groups and singular integrals. II: Singular kernels supported on submanifolds
• Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups. I
• Singular integrals and weighted Triebel-Lizorkin and Besov spaces of arbitrary number of parameters
• Pseudodifferential operators of mixed type adapted to distributions of \(k\)-planes
• Flag Hardy spaces and Marcinkiewicz multipliers on the Heisenberg group
• A multi-dimensional resolution of singularities with applications to analysis
• Some Further Classes of Pseudo-Differential and Singular-Integral Operators Arising in Boundary-Value Problems I Composition of Operators
• Correction to ``Composition and L²-boundedness of flag kernels (Colloq. Math. 118 (2010), 581–585)
• Duality of multiparameter Hardy spaces Hp on spaces of homogeneous type
• Multi-parameter Singular Integrals
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type
• Composition and L²-boundedness of flag kernels
• Lp-boundedness of flag kernels on homogeneous groups
• Analysis of the Hodge Laplacian on the Heisenberg group
• Singular integrals with flag kernels and analysis on quadratic CR manifolds