Date of Graduation

12-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Phillip Harrington

Committee Member

Daniel Luecking

Second Committee Member

Andrew Raich

Abstract

The Diederich-Fornss Index has played a crucial role in studying regularity of the Bergman projection on pseudoconvex domains in Sobolov spaces as is shown by Kohn, Harrington, Pinton and Zampieri and others. In this work, we discuss the Diederich-Fornss Index on Hartogs domains, and its relation to other properties connected to regularity of the Bergman projection. An upper and lower bound for the Diederich-Fornss Index is calculated for Hartogs domains and computed sharply for worm domains. Related conditions for the existence of a strong Stein neighborhood basis for Hartogs domains are introduced.

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