Journal ArticleDOI
Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg
TLDR
In this paper, the dispersive and Strichartz inequalities on the Heisenberg group were proved by the analysis of Besov-type spaces on the group, and the results were extended to the general case.Abstract:
In this paper, we prove dispersive and Strichartz inequalities on the Heisenberg group. The proof involves the analysis of Besov-type spaces on the Heisenberg group.read more
Citations
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Journal ArticleDOI
Sharp constants in several inequalities on the Heisenberg group
Rupert L. Frank,Elliott H. Lieb +1 more
TL;DR: In this article, the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities were derived.
Journal ArticleDOI
Interpolation inequalities in Besov spaces
TL;DR: In this paper, the authors presented new interpolation inequalities in the framework of homogeneous Besov spaces, which reduces those two types as special cases and reduces Miyakawa's inequalitiy.
Journal ArticleDOI
Homogeneous Besov Spaces on Stratified Lie Groups and Their Wavelet Characterization
Hartmut Führ,Azita Mayeli +1 more
TL;DR: In this paper, wavelet characterizations of homogeneous Besov spaces on stratified lie groups, both in terms of continuous and discrete wavelet systems, were established, and the existence of wavelet frames and associated atomic decomposition formulas was proved.
Journal ArticleDOI
Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups
TL;DR: In this paper, it was shown that the propagator behaves like a wave operator on a space of the same dimension p as the center of the group, and like a Schrodinger operator on the same dimensions k as the radical of the canonical skew-symmetric form, which suggests a decay rate of exponant -(k+p-1)/2.
Journal ArticleDOI
Refined Hardy inequalities
TL;DR: In this paper, the authors present refined Hardy inequalities, generalisations of the usual Hardy inequalities that are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same or-der of magnitude.
References
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Book
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals
Elias M. Stein,Timothy S Murphy +1 more
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
Book
Theory of function spaces
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Journal ArticleDOI
Endpoint Strichartz estimates
Markus Keel,Terence Tao +1 more
TL;DR: In this paper, an abstract Strichartz estimate for the wave equation (in dimension n ≥ 4) and for the Schrodinger equation (n ≥ 3) was proved.