Singular and maximal Radon transforms: Analysis and geometry.
An example of the Heisenberg group
Compositions of pseudo-differential operators
Spectral multipliers and multiple-parameter structures on the Heisenberg group
Some oscillatory integrals and their applications
Homogenous distributions on spaces of Hermitean matrices.
Analysis in matrix space and Speh's representations.
Multiparameter singular integrals and maximal functions
We prove -boundedness for a class of singular integral operators and maximal operators associated with a general -parameter family of dilations on . This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.
On the product theory of singular integrals.
We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in...
L-estimates for the wave equation on the Heisenberg group.
Let £ denote the sub-Laplacian on the Heisenberg group H. We prove that e / (1 - £) extends to a bounded operator on L(H), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.
Corrigenda: .
We wish to acknowledge and correct an error in a proof in our paper , which appeared in Revista Matemática Iberoamericana, volume 20, number 2, 2004, pages 531-561.
An algebra of pseudo-differential operators and quantum mechanics in phase space
Nous étudions une algèbre de fonctions infiniment différentiables définies sur l’espace de phase et satisfaisant des conditions de croissance à l’infini. Le produit dans est la transformée de Fourier symplectique de la convolution gauche. On montre que est une généralisation naturelle de l’algèbre des opérateurs pseudodifférentiels.
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