On the variance of the number of real zeros of a random trigonometric polynomial.
On the weak (1,1) boundedness of a class of oscillatory singular integrals
We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include and . Some related counterexample is also discussed.
On weak minima of certain integral functionals
We prove a regularity result for weak minima of integral functionals of the form where F(x,ξ) is a Carathéodory function which grows as with some p > 1.
On weak restricted estimates and endpoints problems for convolutions with oscillating kernels (II)
On weak type inequalities for rare maximal functions
The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.
On weak type inequalities for rare maximal functions in ℝⁿ
The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.
On weakly A-harmonic tensors
We study very weak solutions of an A-harmonic equation to show that they are in fact the usual solutions.
On weighted dyadic Carleson's inequalities.
On weighted estimates for the Kakeya maximal operator
On weighted inequalities for certain fractional integral operators.
On weighted inequalities for ergodic operators
On weighted inequalities for operators of potential type
In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on the homogeneous...
On weighted inequalities for parametric Marcinkiewicz integrals.
On weighted norm inequalities for the maximal function
On weighted norm inequalities for the Riesz transforms of functions with vanishing moments
On weighted norm integral inequality of g. h. Hardy's type
On weighted transplantation and multipliers for Laguerre expansions.
On weighted weak type norm inequalities for one-sided oscillatory singular integrals
We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities for a class of one-sided oscillatory singular integrals with smooth kernel.
Ondelettes et fonctions splines
Ondelettes et poids de Muckenhoupt
We study, for a basis of Hölderian compactly supported wavelets, the boundedness and convergence of the associated projectors on the space for some p in ]1,∞[ and some nonnegative Borel measure μ on ℝ. We show that the convergence properties are related to the criterion of Muckenhoupt.