The weighted estimates for the operators \(V^{\alpha} ( - \Delta _G+V) ^{- \beta}\) and \(V^{\alpha} \nabla _G( - \Delta _G+V)^{ - \beta}\) on the stratified Lie group \(G\)

DOI10.1016/j.jmaa.2008.08.043zbMath1156.35338OpenAlexW2010171045WikidataQ115346212 ScholiaQ115346212MaRDI QIDQ953481

Yu Liu

Publication date: 6 November 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.08.043

zbMATH Keywords

Schrödinger operators\(L^p-L^q\) estimatesreverse Hölder classnonnegative potential

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Elliptic equations on manifolds, general theory (58J05)

Related Items (9)

Schrödinger type operators on generalized Morrey spaces ⋮ The Herz-boundedness of commutators related to Schrödinger operators in the setting of Heisenberg group ⋮ The boundedness of commutators associated with Schrödinger operators on Herz spaces ⋮ On boundedness property of singular integral operators associated to a Schrödinger operator in a generalized Morrey space and applications ⋮ Boundedness of the fractional maximal operator in generalized Morrey space on the Heisenberg group ⋮ Parabolic fractional maximal operator in modified parabolic Morrey spaces ⋮ The higher order Riesz transform and \(BMO\) type space associated with Schrödinger operators on stratified Lie groups ⋮ The weighted \(L^p-L^q\) boundedness of commutators of Schrödinger type operators on the stratified Lie group \(G\) ⋮ A compactness criterion and application to the commutators associated with Schrödinger operators

Cites Work

• Unnamed Item
• Estimates for the operators \(V^{\alpha}(-\Delta +V)^{-\beta}\) and \(V^{\alpha} \nabla(-\Delta +V)^{-\beta}\) with certain non-negative potentials \(V\)
• \(L^p\) estimates of Schrödinger operators on nilpotent groups
• \(L^ p\) estimates for Schrödinger operators with certain potentials
• Hypoelliptic second order differential equations
• The uncertainty principle
• Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• A Remark on Estimates for Uniformly Elliptic Operators on WeightedLp Spaces and Morrey Spaces

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