Related papers: Interpolating sequences for $H^{\infty}(B_H)$

Let $({\mathcal X}, d, \mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors establish an interpolation result that a sublinear operator which…

In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H^p spaces, expressed in terms of the Carleson constants of related scalar measures.…

Given an inner function $B$ we classify the invariant subspaces of the algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of these invariant subspaces for the distance of an element in $L^\infty$ to a certain…

We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over $\mathbb{R}^{n}$ or a half-space in $\mathbb{R}^{n}$ or a bounded Euclidean…

This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…

We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of…

In this work we study Hardy Sobolev spaces in the ball of $C^n$ with respect to interpolating sequences and Carleson measures. We compare them with the classical Hardy spaces of the ball and we stress analogies and differences.

We prove that a suitably adjusted version of Peter Jones' formula for interpolation by bounded holomorphic functions gives a sharp upper bound for what is known as the constant of interpolation. We show how this leads to precise and…

Let $A$ be a sequence of points of $\mathbb{B}^n$ the unit ball in $\mathbb{C}^n.$ In terms of interpolating vectorial function (or Amar's function)[1], we give a necessary condition on $A$ to be interpolating for the weighted Bergman space…

Given an inner function $\theta$, the associated star-invariant subspace $K^\infty_\theta$ is formed by the functions $f\in H^\infty$ that annihilate (with respect to the usual pairing) the shift-invariant subspace $\theta H^1$ of the Hardy…

The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…

The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges-Rovnyak spaces H (b) where the defining function b is a general non-extreme rational function. Our results carry over to recently…

We give a characterization of interpolating sequences for bounded analytic functions on the bidisk.

Let $N$ be the Heisenberg group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a…

We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f converge…

We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.

We generalize a well-known sufficient condition for interpolating sequences for the Hilbert Bergman spaces to other Bergman spaces with normal weights (as defined by Shields and Williams) and obtain new results regarding the membership of…

Let H be a separable Hilbert space with a fixed orthonormal basis (e_n), n>=1, and B(H) be the full von Neumann algebra of the bounded linear operators T: H -> H. Identifying l^\infty = C(\beta N) with the diagonal operators, we consider…

We give a full description of complete interpolating sequences for the shift-invariant space generated by the Gaussian. As a consequence, we rederive the known density conditions for sampling and interpolation.

We consider the problem of complex interpolation of certain Hardy-type subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and $H_{X_1}$ be…