相关论文: Another proof of the corona theorem

The corona problem was motivated by the question of the density of the open unit disc in the maximal ideal space of the algebra of bounded holomorphic functions on the unit disc. The corona problem connects operator theory, function theory,…

Let $\mathbb{I}$ be a proper ideal of $H^{\infty}(\D)$. We prove the corona theorem for infinitely many generators on the algebra $H^{\infty}_{\mathbb{I}}$ in which the corona theorem for finitely many functions is known to hold. This…

Using a description of the spectrum of bidual algebra $A^{**}$ of a uniform algebra $A$ we obtain abstract corona theorem for certain uniform algebras. It asserts the density of a specific Gleason part in the spectrum of an $H^\infty$ --…

We study the structure of the maximal ideal space $M(H^{\infty})$ of the algebra $H^{\infty}=H^{\infty}(\Di)$ of bounded analytic functions defined on the open unit disk $\Di\subset\Co$. Based on the fact that $dim\ M(H^{\infty})=2$ we…

Let $B$ be a Blaschke product. We prove in several different ways the corona theorem for the algebra $H^\infty_B:=\mC+BH^\infty$. That is, we show the equivalence of the classical {\em corona condition} on data $f_1, ..., f_n \in…

The corona problem was motivated by the question of the density of the open unit disk D in the maximal ideal space of the algebra, H1(D), of bounded holomorphic functions on D. In this note we study relationships of the problem with…

We obtain estimates in the corona theorem for the algebra of analytic functions in the unit disc whose nth derivative is bounded, and its subalgebras defined by the boundary continuity of the nth derivative. The corona theorem for such…

Let $E$ be a Banach lattice on $\mathbb Z$ having order continuous norm. We show that for any function $f = \{f_j\}_{j \in \mathbb Z}$ from the Hardy space $H_\infty (E)$ such that $\delta \leqslant \|f (z)\|_E \leqslant 1$ for all $z$ from…

For a wide class of domains $G\subset\mathbb C^d$ including balls and polydisks we prove the density of their canonical image in the spectrum of $H^\infty(G)$. This Corona Theorem is proved first in its abstract version for certain uniform…

We study the $H^{\infty}(\mathbb{B}_{n})$ Corona problem $\sum_{j=1}^{N}f_{j}g_{j}=h$ and show it is always possible to find solutions $f$ that belong to $BMOA(\mathbb{B}_{n})$ for any $n>1$, including infinitely many generators $N$. This…

We prove an $H^2-$Corona theorem with estimate $C(\delta)=C\delta^{-1-q}|\log \delta|$ for $\delta\ll 1$ on delta-regular domains, where $q=\min\{n,m-1\}$ and $m$ is the number of generators. This class of domains includes smooth bounded…

In this paper continuing our work started in our earlier papers we prove the corona theorem for the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.

This paper utilizes Cauchy's transform and duality for the Dirichlet-type space $D(\mu)$ with positive superharmonic weight $U_\mu$ on the unit disk $\mathbb{D}$ to establish the corona theorem for the Dirichlet-type multiplier algebra…

In this paper we consider the matrix-valued $H^{p}$ corona problem in the disk and polydisk. The result for the disk is rather well known, and is usually obtained from the classical Carleson Corona Theorem by linear algebra. Our proof…

Let $A$ be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if $f,f_1,\dots,f_n\in A$ satisfy $|f|\leq \sum_{j=1}^n |f_j|$, does there exist $g_j\in A$ and a constant…

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 $M$ be a non-compact connected Riemann surface of finite type, and $R\subset\subset M$ be a relatively compact domain such that $H_{1}(M,\Z)=H_{1}(R,\Z)$. Let $\tilde R\longrightarrow R$ be a covering. We study the algebra…

Let $D\subset\Co$ be a bounded domain, whose boundary $B$ consists of $k$ simple closed continuous curves and $H^{\infty}(D)$ be the algebra of bounded analytic functions on $D$. We prove the matrix-valued corona theorem for matrices with…

We study the corona problem on the unit ball and the unit polydisc in $\CC^n$. We provide affirmative solutions to both problems.

The main goal of this paper is to give an unified proof of the corona problem on weighted Hardy spaces and on Morrey spaces. We use a technique that allows to reduce the problem to the Hardy spaces $H^2(\theta)$