{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:art_sci_etds-1461"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:art_sci_etds-1461","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"Regularity of the Bergman Projection on Variants of the Hartogs Triangle","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Chen, Liwei"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Steven G Krantz","Steven G Krantz, Carl M Bender, Quo-Shin Chi, Renato Feres, Xiang Tang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-15T07:00:00Z","date_published":"2015-05-15T07:00:00Z","updated_at":"2026-07-24T06:12:08Z","subjects":["Bergman projection","Hartogs triangle","Lp regularity","Muckenhoupt weights","Sobolev regularity","Mathematics"],"languages":["English (en)"],"rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/art_sci_etds/461"],"render_values":[{"text":"https://openscholarship.wustl.edu/art_sci_etds/461","href":"https://openscholarship.wustl.edu/art_sci_etds/461","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/K7707ZMQ","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Steven G Krantz","Steven G Krantz, Carl M Bender, Quo-Shin Chi, Renato Feres, Xiang Tang"]},{"key":"dc:creator","label":"Author","values":["Chen, Liwei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-06-19T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics","Graduate School of Arts and Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Bergman projection","Hartogs triangle","Lp regularity","Muckenhoupt weights","Sobolev regularity","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]},{"key":"dc:rights","label":"Dc Rights","values":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/K7707ZMQ","https://openscholarship.wustl.edu/art_sci_etds/461"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Permanent URL: https://doi.org/10.7936/K7707ZMQ"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Regularity of the Bergman Projection on Variants of the Hartogs Triangle"]}]}],"canonical_facts":{"dc:contributor":["Steven G Krantz","Steven G Krantz, Carl M Bender, Quo-Shin Chi, Renato Feres, Xiang Tang"],"dc:creator":["Chen, Liwei"],"dc:date.available":["2015-06-19T07:00:00Z"],"dc:description":["Permanent URL: https://doi.org/10.7936/K7707ZMQ"],"dc:description.abstract":["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."],"dc:identifier":["https://doi.org/10.7936/K7707ZMQ","https://openscholarship.wustl.edu/art_sci_etds/461"],"dc:language":["English (en)"],"dc:rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"dc:subject":["Bergman projection","Hartogs triangle","Lp regularity","Muckenhoupt weights","Sobolev regularity","Mathematics"],"dc:title":["Regularity of the Bergman Projection on Variants of the Hartogs Triangle"],"thesis:degree_discipline":["Mathematics","Graduate School of Arts and Sciences"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:12:08Z"}