A note on wavelet bases in function spaces
A Note on Wavelets and S-asymptotics
A note on weak estimates for oscillating kernels
A note on weighted estimates for the Schrödinger operator.
A note to the Fourier method of solving partial second-order differential equations
A Paley type inequality for two-parameter Vilenkin-Fourier coefficients.
A particular smooth interpolation that generates splines
There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline...
A partir et autour de Wiener
A proof of Pełczyński's conjecture for the Haar system
A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.
Given a doubling measure μ on Rd, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L2(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition adapted...
A property of Fourier Stieltjes transforms on the discrete group of real numbers
Let be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on . Then for every , has a vanishing interior Lebesgue measure. If the statement is not generally true. The result is applied to prove a theorem of Rosenthal.
-weighted inequalities with Lipschitz and BMO norms.
A radial estimate for the maximal operator associated with the free Schrödinger equation
Let d > 0 be a positive real number and n ≥ 1 a positive integer and define the operator and its associated global maximal operator by , f ∈ (ℝⁿ), x ∈ ℝⁿ, t ∈ ℝ, , f ∈ (ℝⁿ), x ∈ ℝⁿ, where f̂ is the Fourier transform of f and (ℝⁿ) is the Schwartz class of rapidly decreasing functions. If d = 2, is the solution to the initial value problem for the free Schrödinger equation (cf. (1.3) in this paper). We prove that for radial functions f ∈ (ℝⁿ), if n ≥ 3, 0 < d ≤ 2, and p ≥ 2n/(n-2), the...
A refinement of the Helson-Szegö theorem and the determination of the extremal measures
A relation between Fourier transforms in one and two variables
A remark on entropy of Abelian groups and the invariant uniform approximation property
A remark on Fefferman-Stein's inequalities.
It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.
A remark on Fourier-Stieltjes transform
A remark on multiresolution analysis of
A condition on a scaling function which generates a multiresolution analysis of is given.
A Remark on Periodic Tchebyshev Systems.