Perturbations de suites presque-périodiques de nombres réels et mesures étranges sur la droite
Perturbations singulières et noyaux de Poisson
Phase Retrieval Techniques for Radar Ambiguity Problems.
Piecewise Linear Wavelets on Sierpinski Gasket Type Fractals.
Plane waves, biregular functions and hypercomplex Fourier analysis
Poches de tourbillon singulières dans un fluide faiblement visqueux.
In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is C1+s outside a singular set Σ, so the velocity is, for all time, lipschitzian outside the image of Σ through the viscous flow. In addition, the correponding lipschitzian norm is independent of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.
Poincaré inequalities and Sobolev spaces.
Our understanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function.[Proceedings...
Pointwise analysis of Riemann's "nondifferentiable" function.
Pointwise convergence for expansions in surface harmonics of arbitrary dimension.
Pointwise convergence for subsequences of weighted averages
We prove that if μₙ are probability measures on ℤ such that μ̂ₙ converges to 0 uniformly on every compact subset of (0,1), then there exists a subsequence such that the weighted ergodic averages corresponding to satisfy a pointwise ergodic theorem in L¹. We further discuss the relationship between Fourier decay and pointwise ergodic theorems for subsequences, considering in particular the averages along n² + ⌊ρ(n)⌋ for a slowly growing function ρ. Under some monotonicity assumptions, the rate...
Pointwise convergence of multiplier operators
Pointwise convergence to the initial data for nonlocal dyadic diffusions
We solve the initial value problem for the diffusion induced by dyadic fractional derivative in . First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator....
Pointwise ergodic theorems for arithmetic sets
Pointwise estimates for commutator singular integrals
Pointwise Fourier Inversion: a Wave Equation Approach.
Pointwise Fourier Inversion and Localization in ...
Pointwise Fourier inversion of distributions on spheres
Given a distribution on the sphere we define, in analogy to the work of Łojasiewicz, the value of at a point of the sphere and we show that if has the value at , then the Fourier-Laplace series of at is Abel-summable to .
Pointwise Fourier Inversion on Tori and Other Compact Manifolds.
Pointwise multipliers for functions of weighted bounded mean oscillation
Pointwise multipliers for reverse Holder spaces
We classify weights which map reverse Hölder weight spaces to other reverse Hölder weight spaces under pointwise multiplication. We also give some fairly general examples of weights satisfying weak reverse Hölder conditions.