Related papers: On Interpolation by Functions in $\ell^p_A$
We characterize the Carleson measures $\mu$ on the unit disk for which the image of the Hardy space $H^p$ under the corresponding embedding operator is closed in $L^p(\mu)$. In fact, a more general result involving $(p,q)$-Carleson measures…
Let $S$ be a sequence of points in ${\mathbb{D}}^{n}.$ Suppose that $S$ is $H^{p}$ interpolating. Then we prove that the sequence $S$ is Carleson, provided that $p>2.$ We also give a sufficient condition, in terms of dual boundedness and…
Doubling metric measure spaces provide a natural framework for singular integral operators. In contrast, the study of maximally modulated singular integral operators, the so-called Carleson operators, has largely been limited to Euclidean…
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 characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This…
The interpolating sequences for $H^{\infty}({\mathbb{D}}),$ the bounded holomorphic function in the unit disc ${\mathbb{D}}$ of the complex plane ${\mathbb{C}},$ {\small where characterised by L. Carleson by metric conditions on the points.…
Let $A_p(\C)$ be the space of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$ and let $V$ be a discrete sequence of complex numbers which is not a uniqueness set for $A_p(\C)$. We use $L^2$ estimates for the…
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.…
We study real and complex interpolation of abstract Ces\`aro, Copson and Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i} construction for those spaces. The results may be regarded as generalizations of…
Title: On linear extension for interpolating sequences. Author: Eric Amar Abstract: Let A be a uniform algebra on the compact space X and $\sigma $ a probability measure on X. We define the Hardy spaces $H^{p}(\sigma)$ and the…
Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with…
Let (X j , d j , $\mu$ j), j = 0, 1,. .. , m be metric measure spaces. Given 0 < p $\kappa$ $\le$ $\infty$ for $\kappa$ = 1,. .. , m and an analytic family of multilinear operators T z : L p 1 (X 1) x $\bullet$ $\bullet$ $\bullet$ L p m (X…
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of…
We prove that under the extended Carleson's condition, a sequence $(x_n) \subset B_H$ is linear interpolating for $H^{\infty}(B_H)$ for an infinite dimensional Hilbert space H. In particular, we construct the interpolating functions for…
This expository article explores the vital role of interpolation theory and Lorentz spaces in the rigorous analysis of partial differential equations (PDEs). While classical Lebesgue spaces ($L_{p}$) successfully measure the magnitude of…
We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.
Let $B_{\alpha}^{p}$ be the space of $f$ holomorphic in the unit ball of $\Bbb C^n$ such that $(1-|z|^2)^\alpha f(z) \in L^p$, where $0<p\leq\infty$, $\alpha\geq -1/p$ (weighted Bergman space). In this paper we study the interpolating…
In this paper we prove that $M^p_\Lambda$ is almost isometric to $\ell^p$ in the canonical way when $\Lambda$ is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for M\"untz spaces…
Some new characterizations on Carleson measures for weighted Bergman spaces on the unit ball involving product of functions are obtained. For these we characterize bounded and compact Toeplitz operators between weighted Bergman spaces. The…