The Bergman projection in Lp for domains with minimal smoothness

Loredana Lanzani, Elias M. Stein

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Let D⊂ℂn be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove Lp(D)-regularity for the Bergman projection B, and for the operator {pipe}B{pipe} whose kernel is the absolute value of the Bergman kernel with p in the range (1,+∞). As an application, we show that the space of holomorphic functions in a neighborhood of D is dense in θ{symbol}Lp(D). 2013

Original languageEnglish (US)
Pages (from-to)127-154
Number of pages28
JournalIllinois Journal of Mathematics
Volume56
Issue number1
StatePublished - 2012
Externally publishedYes

Fingerprint

Bergman Projection
Bergman Kernel
Pseudoconvex Domain
Absolute value
Smoothness
Analytic function
Regularity
kernel
Operator
Range of data

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Bergman projection in Lp for domains with minimal smoothness. / Lanzani, Loredana; Stein, Elias M.

In: Illinois Journal of Mathematics, Vol. 56, No. 1, 2012, p. 127-154.

Research output: Contribution to journalArticle

@article{a2ba112233ce40bea98a8ce44742f272,
title = "The Bergman projection in Lp for domains with minimal smoothness",
abstract = "Let D⊂ℂn be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove Lp(D)-regularity for the Bergman projection B, and for the operator {pipe}B{pipe} whose kernel is the absolute value of the Bergman kernel with p in the range (1,+∞). As an application, we show that the space of holomorphic functions in a neighborhood of D is dense in θ{symbol}Lp(D). 2013",
author = "Loredana Lanzani and Stein, {Elias M.}",
year = "2012",
language = "English (US)",
volume = "56",
pages = "127--154",
journal = "Illinois Journal of Mathematics",
issn = "0019-2082",
publisher = "University of Illinois at Urbana-Champaign",
number = "1",

}

TY - JOUR

T1 - The Bergman projection in Lp for domains with minimal smoothness

AU - Lanzani, Loredana

AU - Stein, Elias M.

PY - 2012

Y1 - 2012

N2 - Let D⊂ℂn be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove Lp(D)-regularity for the Bergman projection B, and for the operator {pipe}B{pipe} whose kernel is the absolute value of the Bergman kernel with p in the range (1,+∞). As an application, we show that the space of holomorphic functions in a neighborhood of D is dense in θ{symbol}Lp(D). 2013

AB - Let D⊂ℂn be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove Lp(D)-regularity for the Bergman projection B, and for the operator {pipe}B{pipe} whose kernel is the absolute value of the Bergman kernel with p in the range (1,+∞). As an application, we show that the space of holomorphic functions in a neighborhood of D is dense in θ{symbol}Lp(D). 2013

UR - http://www.scopus.com/inward/record.url?scp=84884782645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884782645&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84884782645

VL - 56

SP - 127

EP - 154

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

SN - 0019-2082

IS - 1

ER -