• Publications
  • Influence
Quantization on Nilpotent Lie Groups
Preface.- Introduction.- Notation and conventions.- 1 Preliminaries on Lie groups.- 2 Quantization on compact Lie groups.- 3 Homogeneous Lie groups.- 4 Rockland operators and Sobolev spaces.- 5Expand
  • 150
  • 12
  • PDF
Quantization of Pseudo-differential Operators on the Torus
AbstractPseudo-differential and Fourier series operators on the torus ${{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}$ are analyzed by using global representations by Fourier series instead of localExpand
  • 107
  • 12
  • PDF
Global L 2-Boundedness Theorems for a Class of Fourier Integral Operators
ABSTRACT The local L 2-mapping property of Fourier integral operators has been established in Hörmander (1971) and in Eskin (1970). In this article, we treat the global L 2-boundedness for a class ofExpand
  • 85
  • 8
  • PDF
Introduction to pseudo-differential operators
The present notes give introduction to the theory of pseudo-differential operators on Euclidean spaces. The first part is devoted to the necessary analysis of functions, such as basics of the FourierExpand
  • 59
  • 6
  • PDF
Fourier multipliers on compact Lie groups
In this paper we prove L p Fourier multiplier theorems for invariant and also noninvariant operators on compactLie groups in the spirit of thewell-knownHörmander–Mikhlin theorem on Rn and itsExpand
  • 18
  • 6
  • PDF
Global L2-boundedness theorems for a class of Fourier integral operators
The local $L^2$-mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-boundedness for a class ofExpand
  • 57
  • 5
  • PDF
$$L^p$$Lp Fourier multipliers on compact Lie groups
In this paper we prove $$L^p$$Lp Fourier multiplier theorems for invariant and also non-invariant operators on compact Lie groups in the spirit of the well-known Hörmander–Mikhlin theorem onExpand
  • 25
  • 4
  • PDF
On multipliers on compact Lie groups
In this note we announce Lp multiplier theorems for invariant and noninvariant operators on compact Lie groups in the spirit of the well-known Hörmander-Mikhlin theorem on ℝn and its versions on theExpand
  • 24
  • 3
  • PDF
Hardy, Hardy-Sobolev, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights forExpand
  • 5
  • 3
  • PDF