Related papers: On Lebesgue Constants for Interpolation Points on …
This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder\'on's and Zygmund's theory of first order…
We prove fractional Leibniz rules and related commutator estimates in the settings of weighted and variable Lebesgue spaces. Our main tools are uniform weighted estimates for sequences of square-function-type operators and a bilinear…
Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
We investigate the effect of planar univalent harmonic mappings on the Lebesgue measure of measurable sets in the complex plane. Motivated by Problem 3.25 of Koh and Kovalev (HQM2010), we establish sharp quantitative area distortion…
Estimates are obtained for the Lebesgue constants associated with the Gauss quadrature points on $(-1, +1)$ augmented by the point $-1$ and with the Radau quadrature points on either $(-1, +1]$ or $[-1, +1)$. It is shown that the Lebesgue…
In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in…
A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be…
We consider multipoint Pad\'e approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium…
This is an exposition of a class of problems and results on the number of integral points close to plane curves. We give a detailed proof of a theorem of Huxley and Sargos, following the account of Bordell\`es. Along the way we correct an…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…
The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
The first main result presented in the paper shows that the perimeters of inner parallel sets of planar shapes having a given constant width are minimal for the Reuleaux triangles. This implies that the areas of inner parallel sets and,…
We give a sharp bound for the Lebesgue constant associated to Leja sequences in the complex unit disk, confirming a conjecture made by Calvi and Phung in 2011