The Stieltjes transform of distributions.
The Uncertainty Principle: A Mathematical Survey.
Three results in Dunkl analysis
We first establish a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the norm of Dunkl translations in dimension 1. Finally, we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.
Trace Inequalities, Maximal Inequalities, and Weighted Fourier Transform Estimates.
Transferring eigenfunction bounds from to hⁿ
By using the notion of contraction of Lie groups, we transfer estimates for joint spectral projectors from the unit complex sphere in to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.
Transformée de Fourier et stabilité sur les surfaces abéliennes
Two problems associated with convex finite type domains.
We use scaling properties of convex surfaces of finite line type to derive new estimates for two problems arising in harmonic analysis. For Riesz means associated to such surfaces we obtain sharp Lp estimates for p > 4, generalizing the Carleson-Sjölin theorem. Moreover we obtain estimates for the remainder term in the lattice point problem associated to convex bodies; these estimates are sharp in some instances involving sufficiently flat boundaries.
Two results on the Dunkl maximal operator
In this article, we first improve the scalar maximal theorem for the Dunkl maximal operator by giving some precisions on the behavior of the constants of this theorem for a general reflection group. Next we complete the vector-valued theorem for the Dunkl-type Fefferman-Stein operator in the case by establishing a result of exponential integrability corresponding to the case p = +∞.
Uncertainty principles for integral operators
The aim of this paper is to prove new uncertainty principles for integral operators with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function is highly localized near a single point then (f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function and its integral...
Uncertainty principles for orthonormal bases
In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks...). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.
Variation for the Riesz transform and uniform rectifiability
For integers and , we prove that an -dimensional Ahlfors-David regular measure in is uniformly -rectifiable if and only if the -variation for the Riesz transform with respect to is a bounded operator in . This result can be considered as a partial solution to a well known open problem posed by G. David and S. Semmes which relates the boundedness of the Riesz transform to the uniform rectifiability of .
Vibrations de classe Cs 2 des tores plats de dimension s et théorie des nombres.
Weak type endpoint bounds for Bochner-Riesz multipliers.
Weighted norm inequalities and homogeneous cones
Weyl transforms associated with the Riemann-Liouville operator.
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
Zeta-Function and analytic renormalization
Лежандрова униформизация многозначных аналитических функций
Метод разрывных решений в теории пластин
О методе суммирования типа Абеля-Пуассона кратных интегралов Фурье