On Baica's trigonometric identity.
On bases and unconditional bases in the spaces ,1≤p<∞
On belonging of trigonometric series to Orlicz space.
On Bernstein's Inequality and Kahane's Ultraflat Polynomials.
On Besov-Hardy-Sobolev spaces of analytic functions in the unit disc
On bilinear Littlewood-Paley square functions.
On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove thatΣ∞n=-∞ ||Sn(f,g)||22 ≤ C2||f||p2||g||q2.The constant C depends only upon k.
On Billard's Theorem for Random Fourier Series
We show that Billard's theorem on a.s. uniform convergence of random Fourier series with independent symmetric coefficients is not true when the coefficients are only assumed to be centered independent. We give some necessary or sufficient conditions to ensure the validity of Billard's theorem in the centered case.
On block recursions, Askey's sieved Jacobi polynomials and two related systems
Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.
On BMO-regular couples of lattices of measurable functions
We introduce a new “weak” BMO-regularity condition for couples (X,Y) of lattices of measurable functions on the circle (Definition 3, Section 9), describe it in terms of the lattice , and prove that this condition still ensures “good” interpolation for the couple of the Hardy-type spaces corresponding to X and Y (Theorem 1, Section 9). Also, we present a neat version of Pisier’s approach to interpolation of Hardy-type subspaces (Theorem 2, Section 13). These two main results of the paper are...
On Bojarski's index formula for nonsmooth interfaces.
On boundedness properties of certain maximal operators
It is known that the weak type (1,1) for the Hardy-Littlewood maximal operator can be obtained from the weak type (1,1) over Dirac deltas. This theorem is due to M. de Guzmán. In this paper, we develop a technique that allows us to prove such a theorem for operators and measure spaces in which Guzmán's technique cannot be used.
On bounds for the derivates of a complex-valued function on a compact interval.
On (C,1) summability for Vilenkin-like systems
We give a common generalization of the Walsh system, Vilenkin system, the character system of the group of 2-adic (m-adic) integers, the product system of normalized coordinate functions for continuous irreducible unitary representations of the coordinate groups of noncommutative Vilenkin groups, the UDMD product systems (defined by F. Schipp) and some other systems. We prove that for integrable functions σₙf → f (n → ∞) a.e., where σₙf is the nth (C,1) mean of f. (For the character system of the...
On (C,1) summability of integrable functions with respect to the Walsh-Kaczmarz system
Let G be the Walsh group. For we prove the a. e. convergence σf → f(n → ∞), where is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, , where H is the Hardy space on the Walsh group.
On Calderón's conjecture.
On Calderón-Toeplitz Operators.
On certain estimates for Marcinkiewicz integrals and extrapolation.
On certain Heun functions, associated functions of discrete variables, and applications.
On certain hypersingular integrals
On certain linear combinations of partial sums of Fourier series