Date of Graduation

12-2010

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Loredana Lanzani

Committee Member

Luca Capogna

Second Committee Member

Phillip S. Harrington

Keywords

Applied sciences, Pure sciences, Complex dimension n, Convex domain, Hardy space, Holomorphic functions, Integral representations

Abstract

This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are strongly convex with real boundary of class C^2. We obtain integral representations utilizing the Leray kernel for Hardy space (p=1) functions on such domains D. Next we define an operator to prove the non-tangential limits of a function in Hardy space (p between 1 and infinity, inclusive) of domain D integrated against any Lipschitz function is also in said space above, once again utilizing the Leray kernel. This result yields a separation of singularities for any function f in the Hardy space (p between 1 and infinity, inclusive) space on domain D.

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