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UID:046a6311dc55c56f3c11f326ab1c3d0d
CATEGORIES:Complex Analysis and Geometry Seminar
CREATED:20230329T102447
SUMMARY:Projection operators on \(L^p\)-Bergman spaces of Reinhardt domains
LOCATION:Hill Center Room 705
DESCRIPTION:<div style="border: 0px; font-style: normal; font-weight: 400; font-size: 1
 5px; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web (West Eur
 opean)', 'Segoe UI', -apple-system, 'system-ui', Roboto, 'Helvetica Neue', 
 sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; color: #24
 2424; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0
 px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px
 ; background-color: #ffffff;">Abstract: It is a famous result&nbsp; of M. R
 iesz that the Szego projection operator, initially defined as the orthogona
 l projection from the space \(L^2(\mathbb{T})\) of square integrable functi
 ons on the circle to the Hardy space \(H^2(\mathbb{D}) \),&nbsp; extends&nb
 sp;</div><div style="border: 0px; font-style: normal; font-weight: 400; fon
 t-size: 15px; line-height: inherit; font-family: 'Segoe UI', 'Segoe UI Web 
 (West European)', 'Segoe UI', -apple-system, 'system-ui', Roboto, 'Helvetic
 a Neue', sans-serif; margin: 0px; padding: 0px; vertical-align: baseline; c
 olor: #242424; letter-spacing: normal; orphans: 2; text-align: start; text-
 indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spa
 cing: 0px; background-color: #ffffff;">continuously as a projection operato
 r from \(L^p(\mathbb{T})\) onto \(H^p(\mathbb{D})\). There is a long histor
 y&nbsp;of similar results in the setting of Bergman spaces, and a long list
  of domains where an analogous statement does not hold in the Bergman setti
 ng. We try to understand the geometric distinction between&nbsp;the Hardy a
 nd the Bergman situations in \(L^p\), and propose a new projection operator
  on Reinhardt domains which is expected to have better mapping properties. 
 We verify that the new operator satisfies \(L^p\) estimates in some situati
 ons where the Bergman projection operator does not satisfy such estimates.&
 nbsp; This is joint work with Luke Edholm of the University of Vienna.</div
 >
CONTACT:Debraj Chakrabarti (Central Michigan U.)
DTSTAMP:20260907T041446
DTSTART;TZID=America/New_York:20230331T103000
DTEND;TZID=America/New_York:20230331T113000
SEQUENCE:0
TRANSP:OPAQUE
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