Study of the extension of holomorphic functions from submanifolds of a pseudoconvex domain

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The purpose of the study is to extend holomorphic functions in a submanifold of a pseudoconvex domain D to a holomorphic function in D which belongs to some function spaces and to estimate solutions of the ∂ problem in D. I obtained the L^p extension of holomorphic functions in a submanifold of D to the entire domain D, when D is a strictly pseudoconvex domain in C^n with non-smooth boundary. I studied in the following way. At first, I considered Koppelman's integral formula over ∂D for a holomorphic function in D when -D is a strictly pseudoconvex domain in C^n with smooth boundary. Then by using Stokes' formula, Koppelman's formula is represented by the integral over D. Since a strictly pseudoconvex domain D with non-smooth boundary is approximated by a sequence of strictly pseudoconvex domains with smooth boundary {Dm}, an L^p holomorphic function f in X = {z_n = 0}∩D can be represented by the limit of the integral over X_m = {z_n ― 0}∩D_m. Since the kernel of the integrals is holomorphic in D, f can be extended to a holomorphic function in D. In order to prove that the extended function is an L^p function, we used the method of Schmalz in which he estimated the volume form near the singular points. It seams to me that the same method is applicable to the H^p extension from submanifolds in a strictly pseudoconvex domain in C^n with non-smooth boundary. I will continue the study of the H^p extension. On the other hand, I obtained optimal L^p estimates for ∂ problem in real ellipsoids by using Shaw's technique.