The main purpose of this note is to give a new characterization of the well-known Carleson measure in terms of the integral for functions with their derivatives on the unit ball.
Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in . The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop’s property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.
Boundary values of zero-smooth Besov analytic functions in the unit ball of are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.
Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.
We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces , where is a smooth, bounded convex domain of finite type in ℂⁿ, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.
Let Ω be a C∞-domain in Cn. It is well known that a holomorphic function on Ω behaves twice as well in complex tangential directions (see [GS] and [Kr] for instance). It follows from well known results (see [H], [RS]) that some converse is true for any kind of regular functions when Ω satisfies(P) The real tangent space is generated by the Lie brackets of real and imaginary parts of complex tangent vectorsIn this paper we are interested in the behavior of holomorphic Hardy-Sobolev functions in...