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Advances in AnalysisThe Legacy of Elias M. Stein$
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Advances in Analysis: The Legacy of Elias M. Stein

Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Print publication date: 2014

Print ISBN-13: 9780691159416

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159416.001.0001

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Diagonal Estimates for Bergman Kernels in Monomial-Type Domains

Diagonal Estimates for Bergman Kernels in Monomial-Type Domains

Chapter:
(p.402) Chapter Fifteen Diagonal Estimates for Bergman Kernels in Monomial-Type Domains
Source:
Advances in Analysis
Author(s):

Alexander Nagel

Malabika Pramanik

, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159416.003.0015

This chapter discusses diagonal estimates for Bergman kernels in monomial-type domains. It begins by briefly recalling the definition and some of the elementary properties of the Bergman projection and Bergman kernel. The chapter then turns to a problem which requires obtaining uniform estimates for a Bergman kernel on the diagonal of a model monomial domain. The chapter then sketches an approach devised by Gregor Herbort in 1983, when he gave an example in which the growth of the Bergman kernel on the diagonal is not given by a negative power of the distance to the boundary. Through Herbort's method, the chapter arrives at its required estimates.

Keywords:   Bergman kernels, model monomial domain, monomial-type domains, diagonal estimates, Bergman projection, Gregor Herbort

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