Regularity of the Bergman Projection on Variants of the Hartogs Triangle

The Bergman projection is the orthogonal projection from the space of square integrable functions onto the space of square integrable holomorphic functions on a domain. Initially, the projection is defined on the L2 space, but its behavior on other function spaces, e.g. Lp, Sobolev and Holder spaces, is of considerable interest.In this dissertation, we focus on the Hartogs triangle which is a classical source of counterexamples in several complex variables, and generalize it to higher dimensions. We investigate the Lp mapping properties of the weighted Bergman projections on these Hartogs domains. As applications, we obtain the Lp regularity of the twisted-weighted Bergman projections and the weighted Lp Sobolev regularity of the ordinary Bergman projection on the corresponding domains.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2015

Author dc:creator

• Chen, Liwei

Contributors dc:contributor

• Steven G Krantz
• Steven G Krantz, Carl M Bender, Quo-Shin Chi, Renato Feres, Xiang Tang

• Bergman projection
• Hartogs triangle
• Lp regularity
• Muckenhoupt weights
• Sobolev regularity
• Mathematics

Statement dc:rights

• I have not registered my thesis with the U.S. Copyright Office, and do not intend to.

Language dc:language

English (en)

Identifier

https://openscholarship.wustl.edu/art_sci_etds/461

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:art_sci_etds-1461