On the utility of the Telyakovskiĭ's class .
On the variance of the number of real roots of a random trigonometric polynomial.
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 the weak space and singular measures
We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak space; symmetric sets of constant ratio occur in an unexpected way.
On the weighted estimate of the Bergman projection
We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.
On three problems from the Scottish Book connected with orthogonal systems
On unconditional convergence of Haar series
On uniform convergence of Fourier series.
On uniform convergence of Hermite series
On vector-valued Fourier multiplier theorems
On vector-valued Hardy martingales and a generalized Jensen's inequality.
On Wavelet Sets.
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