Download this article
 Download this article For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Boundary regularity of Bergman kernel in Hölder space

Ziming Shi

Vol. 324 (2023), No. 1, 157–206
DOI: 10.2140/pjm.2023.324.157
Abstract

Let D be a bounded strictly pseudoconvex domain in n. Assuming bD Ck+3+α where k is a nonnegative integer and 0 < α 1, we show that (1) the Bergman kernel B(,w0) Ck+min {α,12}(D¯), for any w0 D and (2) the Bergman projection on D is a bounded operator from Ck+β(D¯) to Ck+min {α,β2}(D¯) for any 0 < β 1. Our results both improve and generalize the work of E. Ligocka.

Keywords
Bergman kernel, Bergman projection, strictly pseudoconvex domain
Mathematical Subject Classification
Primary: 32A25
Secondary: 32T15
Milestones
Received: 7 August 2022
Revised: 8 February 2023
Accepted: 14 April 2023
Published: 22 June 2023
Authors
Ziming Shi
Department of Mathematics
Rutgers University – New Brunswick
Piscataway, NJ
United States

Open Access made possible by participating institutions via Subscribe to Open.