On an infinite linear combination of partial sums of Fourier series
On an integral formula of Berndtsson related to the inversion of the Fourier-Laplace transform of -closed -forms
We give a proof of an integral formula of Berndtsson which is related to the inversion of Fourier-Laplace transforms of -closed -forms in the complement of a compact convex set in .
On an integral of Marcinkiewicz
On analytic rapidly decreasing functions of a real variable
Condizione necessaria e sufficiente affinché una funzione rapidamente decrescente di variabile reale sia uniformemente analitica è che per i suoi coefficienti di Fourier-Hermite riesca per abbastanza piccolo.
On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol.
On approach regions for the conjugate Poisson integral and singular integrals
Let ũ denote the conjugate Poisson integral of a function . We give conditions on a region Ω so that , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that is a bounded operator on , 1 < p < ∞, and is weak (1,1).
On approximate differentiability of functions with bounded deformation.
On Approximation Of Continuous And Differentiable Functions By Fourier-Jacobi Series
On approximation of functions by generalized Abel--Poisson operators.
On approximation of locally compact groups by finite algebraic systems.
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.