Besov spaces and Strichartz estimates on the Heisenberg group

DOI10.1007/BF02791223zbMath0965.22010MaRDI QIDQ5926431

Patrick Gérard, Hajer Bahouri, Chao-Jiang Xu

Publication date: 29 July 2001

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

wave equationHeisenberg groupStrichartz estimation

Mathematics Subject Classification ID

Wave equation (35L05) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Analysis on real and complex Lie groups (22E30)

Related Items (45)

OBSERVABILITY OF BAOUENDI–GRUSHIN-TYPE EQUATIONS THROUGH RESOLVENT ESTIMATES ⋮ Triebel-Lizorkin spaces with variable smoothness and integrability on Lie groups of polynomial growth ⋮ Interpolation inequalities in Besov spaces ⋮ Estimations optimales du noyau de la chaleur sur les groupes de type Heisenberg ⋮ Logarithmic Littlewood-Paley Decomposition and Applications to Orlicz Spaces ⋮ Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian ⋮ Phase-space analysis and pseudo-differential calculus on the Heisenberg group ⋮ Decay estimates for fractional wave equations on \(H\)-type groups ⋮ Strichartz estimates and Fourier restriction theorems on the Heisenberg group ⋮ Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups ⋮ Estimates for the linear viscoelastic damped wave equation on the Heisenberg group ⋮ Decay estimates for a class of wave equations on the Heisenberg group ⋮ Spectral summability for the quartic oscillator with applications to the Engel group ⋮ Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group ⋮ Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group ⋮ Semi-classical analysis on H-type groups ⋮ A survey of the Szegő equation ⋮ Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups ⋮ Improved Sobolev inequalities and Muckenhoupt weights on stratified Lie groups ⋮ Decay estimates for the linear damped wave equation on the Heisenberg group ⋮ On a class of semilinear evolution equations for vector potentials associated with Maxwell's equations in Carnot groups ⋮ Strichartz estimates on the quaternion Heisenberg group ⋮ Homogeneous Besov spaces on stratified Lie groups and their wavelet characterization ⋮ Sharp constants in several inequalities on the Heisenberg group ⋮ Strichartz inequalities for the wave equation with the full Laplacian on H-type groups ⋮ The trace problem for Sobolev spaces over the Heisenberg group ⋮ Towards semi-classical analysis for sub-elliptic operators ⋮ Wave equation on Riemannian symmetric spaces ⋮ An existence and uniqueness result for the Navier-Stokes type equations on the Heisenberg group ⋮ Observability and controllability for the Schrödinger equation on quotients of groups of Heisenberg type ⋮ Unnamed Item ⋮ Multipliers for Besov spaces on graded Lie groups ⋮ Embedding the Heisenberg group into a bounded-dimensional Euclidean space with optimal distortion ⋮ Besov spaces associated with Dunkl's operator ⋮ Radially symmetric traveling waves for the Schrödinger equation on the Heisenberg group ⋮ Trace theorem on the Heisenberg group ⋮ Wave equation on Riemannian symmetric spaces ⋮ Generalized homogeneous Besov spaces associated with the Riemann–Liouville operator ⋮ Strichartz estimates with loss of derivatives under a weak dispersion property for the wave operator ⋮ On the orbital stability of a family of traveling waves for the cubic Schrödinger equation on the Heisenberg group ⋮ Quantum evolution and sub-Laplacian operators on groups of Heisenberg type ⋮ Strichartz estimates for the Schrödinger equation for the sublaplacian on complex spheres ⋮ Generalized Besov type spaces on the dual of the Laguerre hypergroup ⋮ Generalized Besov type spaces on the Laguerre hypergroup ⋮ Potential Spaces on Lie Groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear small data scattering for the wave and Klein-Gordon equation
• A restriction theorem for the Heisenberg group
• Existence of solutions for Schrödinger evolution equations
• Space-time decay for solutions of wave equations
• Hypoelliptic differential operators and nilpotent groups
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets
• Generalized Strichartz inequalities for the wave equation
• A priori estimates for the wave equation and some applications
• The wave equation on the heisenberg group
• A functional calculus for Rockland operators on nilpotent Lie groups
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Fourier analysis on the Heisenberg group
• Endpoint Strichartz estimates
• Inclusions de sobolev en calcul de weyl-hörmander et champs de vecteurs sous-elliptiques
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)

This page was built for publication: Besov spaces and Strichartz estimates on the Heisenberg group