A balanced proper modification of P3.
In this paper we consider the map L defined on the Bergman space [...] of the right half plane [...] .
Let D ⊂ ℂⁿ and be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this result to N-fold...
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.
We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.