Related papers: Extremely weak interpolation in $H^{\infty}$

We prove that, unless assuming additional set theoretical axioms, there are no reflexive space without unconditional sequences of density the continuum. We give for every integer $n$ there are normalized weakly-null sequences of length…

The commonly quoted error rates for QMC integration with an infinite low discrepancy sequence is $O(n^{-1}\log(n)^r)$ with $r=d$ for extensible sequences and $r=d-1$ otherwise. Such rates hold uniformly over all $d$ dimensional integrands…

This paper proposes a novel variant of hyperinterpolation, called hard thresholding hyperinterpolation. This approximation scheme of degree $n$ leverages a hard thresholding operator to filter all hyperinterpolation coefficients, which…

In this note we present a new proof of the Carleson Embedding Theorem on the unit disc and unit ball. The only technical tool used in the proof of this fact is Green's formula. The starting point is that every Carleson measure gives rise to…

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for…

Let $\mathcal X$ be a complete space of homogeneous type. In this note, we prove that the weak$^*$-convergence is true in the Hardy space $H^1(\mathcal X)$ of Coifman and Weiss.

This note discusses an interpolation technique for univariate distributions. In other words, the question is how to obtain a good approximation for f(x|a) if a0 < a < a1 is a control variable and f(x|a0) and f(x|a1) are known. The technique…

Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…

This paper gives a complete answer to the following problem: Find the circle companion of the Hardy space of the unit disk with values in the space of all bounded linear operators between two separable Hilbert spaces. Classically, the…

We characterise interpolating and sampling sequences for the spaces of entire functions f such that f e^{-phi} belongs to L^p(C), p>=1 (and some related weighted classes), where phi is a subharmonic weight whose Laplacian is a doubling…

We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is…

Let $U:[0,\infty)^2 \to [0,\infty)$ be a~measurable kernel satisfying: (i) $U(x,y)$ is nonincreasing in $x$ and nondecreasing in $y$; (ii) there exists a~constant $\theta>0$ such that $U(x,z) \le \theta\left( U(x,y)+U(y,z) \right)$ for all…

We study estimates for Hardy space norms of analytic projections. We first find a sufficient condition for the Bergman projection of a function in the unit disc to belong to the Hardy space $H^p$ for $1 < p < \infty$. We apply the result to…

Following Gorkin, Mortini, and Nikolski, we say that an inner function $I$ in $H^\infty$ of the unit disc has the WEP property if its modulus at a point $z$ is bounded from below by a function of the distance from $z$ to the zero set of…

We study the question of when two weighted variable exponent Bergman spaces or Hardy spaces are equivalent. As an application, we show that variable exponent Hardy spaces have a close relation to classical Hardy spaces when the exponent is…

Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…

In this paper we state the weighted Hardy inequality \begin{equation*} c\int_{{\mathbb R}^N}\sum_{i=1}^n \frac{\varphi^2 }{|x-a_i|^2}\, \mu(x)dx\le \int_{{\mathbb R}^N} |\nabla\varphi|^2 \, \mu(x)dx +k \int_{\mathbb{R}^N}\varphi^2 \,…

Let $(X, Y)$ be a suitable couple of quasi-Banach lattices of measurable functions on $\mathbb T \times \Omega$, and let $(X_A, Y_A)$ be the couple of the corresponding Hardy-type spaces. It has long been suspected that the BMO-regularity…

Let {(Z_i,W_i):i=1,...,n} be uniformly distributed in [0,1]^d * G(k,d), where G(k,d) denotes the space of k-dimensional linear subspaces of R^d. For a differentiable function f from [0,1]^k to [0,1]^d we say that f interpolates (z,w) in…

We prove that Ces\`{a}ro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space $H_{p}$ for $% 0<p<1/\left( 1+\alpha \right).$