On equivalence of \(L^{p}\)-norms related to Schrödinger type operators on Riemannian manifolds

DOI10.1007/s00440-005-0437-4zbMath1094.53034OpenAlexW2090463721MaRDI QIDQ2498922

Ichiro Shigekawa, Tomohiro Miyokawa

Publication date: 11 August 2006

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-005-0437-4

zbMATH Keywords

Littlewood-Paley inequalitiespotential functiondefective intertwining

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Littlewood-Paley-Stein functions for non-local Schrödinger operators ⋮ Cauchy problem for nonlinear Schrödinger equations with inverse-square potentials ⋮ Defective intertwining property and generator domain

Cites Work

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• Invariance of closed convex sets and domination criteria for semigroups
• Defective intertwining property and generator domain
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Littlewood-Paley-Stein inequality for a symmetric diffusion
• Sobolev spaces on a Riemannian manifold and their equivalence
• Integrability of functionals of Dirichlet processes, probabilistic representations of semigroups, and estimates of heat kernels
• \(L^p\) contraction semigroups for vector valued functions
• Dirichlet forms and symmetric Markov processes
• \(L^ p\) contraction semigroups for vector valued functions
• \(L^ p\) estimates for Schrödinger operators with certain potentials
• Estimates in L^p for magnetic Schrodinger operators
• Riemannian geometry and geometric analysis

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