Hong Rae Cho

Holomorphic mean Lipschitz spaces and Hardy–Sobolev spaces on the unit ball

We study two classes of holomorphic functions in the unit ball 𝔹 n of ℂ n : mean Lipschitz spaces and Hardy–Sobolev spaces. Main results include new characterizations in terms of fractional radial differential operators and various comparisons between these two classes.

Products of Toeplitz operators on the Fock space

Let f and g be functions, not identically zero, in the Fock space F 2 α of C. We show that the product TfTg of Toeplitz operators on F 2 α is bounded if and only if f(z) = e q(z) and g(z) = ce−q(z), where c is a nonzero constant and q is a linear polynomial.

A counterexample to the Lρ extension of holomorphic functins from subvarieties to pseudoconvex domains

Using Sibonys example, we get a counterexample to the Lρ (2<p <∞)extension of holomorphic functions from complex linear subspaces to pseudoconvex domains in

Lipschitz and BMO extensions of holomorphic functions from subvarieties to a convex domain

Let be a bounded convex domain with C∞ boundary. Let M be a sub variety in D of dimension one which has no singular points on ∂M and intersects ∂D transversally. Assume that D is weakly totally convex in the complex tangential directions at any point in ∂M We get Lipschitz and BMO extensions of holomorphic functions from M to D

Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces

Let and . We prove that the Segal-Bargmann transform is a bounded operator from fractional Hermite-Sobolev spaces to fractional Fock-Sobolev spaces .

A norm equivalence for the mixed norm of Fock type

In this paper, we prove that the mixed norm for an exponential type weighted integral of an entire function is equivalent to the mixed norm of its radial derivative and the distortion function from the weight function in the n-dimensional complex space.

Holomorphic approximation and holomorphic convexity on pseudoconvex complex manifolds

Let Ω be a complex submanifold with C 3 pseudoconvex boundary such that there is a function λ∊C 3 which is strongly plurisubharmonic in a neighborhood of the boundary of Ω. We prove the Oka-Weil approximation theorem on Ω. Also we show that Ω is holomorphically convex and that the plurisubharmonic hull and the holomorphic hull coincide for Ω. The methods of proof of the above results rely on the elementary -estimates introduced by Hormander ([2], [3])