Characterizations of localized BMO(\({\mathbb R}^n\)) via commutators of localized Riesz transforms and fractional integrals associated to Schrödinger operators

DOI10.1007/BF03191227zbMath1201.42011MaRDI QIDQ847030

Dong Yong Yang, Da Chun Yang

Publication date: 11 February 2010

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/43830

zbMATH Keywords

maximal operatorSchrödinger operatoradmissible functionfractional integralcommutatorRiesz transform\({BMO}_{\rho}({\mathbb{R}}^n)\)

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Schrödinger operator, Schrödinger equation (35J10)

Related Items (7)

Endpoint estimates for commutators of singular integrals related to Schrödinger operators ⋮ \(\operatorname{bmo}_{\rho}(\omega)\) spaces and Riesz transforms associated to Schrödinger operators ⋮ Weighted \(L^p\)-boundedness and \(L^p\)-compactness criteria to commutators of operators with kernels satisfying Hörmander type estimates ⋮ Variation operators for semigroups and Riesz transforms on \(BMO\) in the Schrödinger setting ⋮ The higher order Riesz transform and \(BMO\) type space associated with Schrödinger operators on stratified Lie groups ⋮ Wavelets, Sobolev multipliers, and application to Schrödinger type operators with nonsmooth potentials ⋮ Sharp weighted inequalities for multilinear fractional maximal operators and fractional integrals

Cites Work

• Unnamed Item
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• Localized BMO and BLO spaces on RD-spaces and applications to Schrödinger operators
• Endpoint properties of localized Riesz transforms and fractional integrals associated to Schrödinger operators
• Hardy space \(H^1\) associated to Schrödinger operator with potential satisfying reverse Hölder inequality
• Factorization theorems for Hardy spaces in several variables
• Mean oscillation and commutators of singular integral operators
• A local version of real Hardy spaces
• BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality
• \(L^ p\) estimates for Schrödinger operators with certain potentials
• \(L^p\) boundedness of commutators of Riesz transforms associated to Schrödinger operator
• The uncertainty principle
• On functions of bounded mean oscillation
• Duality of Hardy and BMO spaces associated with operators with heat kernel bounds
• New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications

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