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.