Related papers: On the corona problem for strongly pseudoconvex do…
We study the corona problem on the unit ball in $\CC^n$, and more generally on strongly pseudoconvex domains in $\CC^n$. When the corona problem has just two pieces of data, and an extra geometric hypothesis is satisfied, then we are able…
We prove that the $\mathcal{H}^p$-corona problem has a solution for convex domains of finite type in $\mathbb{C}^n$, $n \ge 2$.
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…
We solve the $\partial\bar{\partial}$-problem for extensible currents defined on a strongly pseudoconvex domain of a contractible manifold.
A sufficient condition for $\bar{\partial}$ to have closed range is given for pseudoconvex, possibly unbounded domains in $\mathbb{C}^n$.
We show that a smooth bounded domain in $\mathbb{C}^n$ admitting partial pseudoconvex exhaustion remains partial pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-$q$-convex domains. Furthermore, we…
We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain,…
In this note we show that if the Corona data depends continuously (smoothly) on a parameter, the solutions of the corresponding Bezout equations can be chosen to have the same smoothness in the parameter.
The Serre problem for a class of hyperbolic pseudoconvex Reinhardt domains in $\Bbb C^2$ as fibers is solved.
This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant boundary conditions are imposed on the single component of the boundary when the domain…
A characterization of non-hyperbolic pseudoconvex Reinhardt domains in $\mathbb C^2$ for which the answer to the Serre problem is positive is given.
We provide sharp and explicit characterizations of the normal cone to sublevel sets of suprema of arbitrary functions, expressed exclusively in terms of subdifferentials of the data functions. In the convex case, the resulting formulas…
We solve the $\partial \bar{\partial}$-problem for the differential forms of class $C^\infty$ with boundary value in currents sense defined on a contractible completely strictly pseudoconvex domain of a complex manifold.
We prove that an open set $D$ in $\C^n$ is pseudoconvex if and only if for any $z\in D$ the largest balanced domain centered at $z$ and contained in $D$ is pseudoconvex, and consider analogues of that characterization in the linearly convex…
For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\partial}$-Neumann problem. The paper extends to domains which are not…
We solve the $\partial \bar{\partial}$-problem for a form with distribution boundary value on a strongly pseudoconvex contractible domain of a complex manifold.
In this paper, we provide some characterizations of strong pseudoconvexity by the boundary behavior of intrinsic invariants for smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As a consequence, if such domain is…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
By modifying Cole's example, we construct explicit Riemann surfaces with large bounds on corona solutions in an elementary way.
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…