Szegö and Bergman projections on non-smooth planar domains
type: Item
instance of: scholarly article
title: Szegö and Bergman projections on non-smooth planar domains
zbMATH Open document ID: 1046.30023
DOI: 10.1007/BF02921866
author: Loredana Lanzani
author: Elias M. Stein
published in: The Journal of Geometric Analysis
publication date: 2004-06-08T00:00:00Z
review text: The paper studies the \(L^p\) boundedness for the Szegő and Bergman projections of a simply connected planar domain in any of the following classes: vanishing chord arc; Lipschitz; Ahlfors regular; or local graph. As an application, the \(L^p\) boundedness for the Riesz transforms is also discussed.
Mathematics Subject Classification ID: 30E25
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 31A10
Mathematics Subject Classification ID: 30C20
Mathematics Subject Classification ID: 30C40
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 2070480
zbMATH Keywords: Bergman projection
zbMATH Keywords: Szegő projection
zbMATH Keywords: simply connected domain
reviewed by: Kehe Zhu
MaRDI profile type: Publication
cites work: Q4039801
cites work: Harmonic measure, \(L^ 2\) estimates and the Schwarzian derivative
cites work: L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
cites work: Factorization theorems for Hardy spaces in several variables
cites work: The mapping theorems of Carathéodory and Lindelöf
cites work: Opérateurs intégraux singuliers sur certaines courbes du plan complexe
cites work: Q3922907
cites work: Q5187597
cites work: The dual of a Bergman space on simply connected domains.
cites work: The failure of \(L^ p\) estimates for harmonic measure in chord-arc domains
cites work: Hardy spaces, $A_\infty$, and singular integrals on chord-arc domains
cites work: The inhomogeneous Dirichlet problem in Lipschitz domains
cites work: Q3320634
cites work: Weighted H p Spaces on Lipschitz Domains
cites work: Q4305610
cites work: The Cauchy kernel, the Szegö kernel, and the Riemann mapping function
cites work: The Poisson integral for generalized half-planes and bounded symmetric domains
cites work: Szego projection versus potential theory for non-smooth planar domains
cites work: Q4508917
cites work: Q4000499
cites work: On univalent functions, Bloch functions and VMOA
cites work: Q3861685
cites work: Q3142876
cites work: Q5607484
cites work: Counterexamples to two variants of the Helson-Szegö theorem.
cites work: Représentation conforme et courbes presque lipschitziennes
cites work: Q3254471
description: scientific article; zbMATH DE number 2070480