Maximal inequalities and Riesz transform estimates on \(L^p\) spaces for Schrödinger operators with nonnegative potentials

DOI10.5802/aif.2320zbMath1161.35003arXivmath/0605047OpenAlexW2031922801MaRDI QIDQ2466307

Besma Ben Ali, Pascal Auscher

Publication date: 14 January 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605047

zbMATH Keywords

Schrödinger operatorsmaximal inequalitiesreverse Hölder estimatesRiesz transforms, Fefferman-Phong inequality

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An \(L^ p\) theory for Schrödinger operators with nonnegative potentials
• Weighted norm inequalities, off-diagonal estimates and elliptic operators. I: General operator theory and weights
• Endpoint estimates for Riesz transforms of magnetic Schrödinger operators
• Absorption semigroups, their generators, and Schrödinger semigroups
• Singular integral operators with non-smooth kernels on irregular domains
• Weighted Hardy spaces
• Schrödinger operators with \(L^p_{loc}\)-potentials
• On \(L^p\) estimates for square roots of second order elliptic operators on \(\mathbb R^n\)
• Riesz transform, Gaussian bounds and the method of wave equation
• Bounds of Riesz transforms on \(L^p\) spaces for second order elliptic operators.
• Semi-linear second-order elliptic equations in \(L^1\)
• \(L^ p\) estimates for Schrödinger operators with certain potentials
• Schrödinger operators with singular potentials
• \(H^p\) spaces of several variables
• Semigroup kernels, Poisson bounds, and holomorphic functional calculus
• The uncertainty principle
• Resolution of a semilinear equation in L¹
• Hardy-Littlewood inequality for quasiregular mappings in certain domains in R^n
• Change of Variable Results for A p -and Reverse Holder RH r -Classes
• Riesz transforms for $1\le p\le 2$
• A multiplier theorem for Schrödinger operators
• On square functions associated to sectorial operators