Weighted Lp estimates for the Bergman and Szegő projections on strongly pseudoconvex domains with near minimal smoothness

Nathan A. Wagner; Brett D. Wick

doi:10.1016/j.aim.2021.107745

Weighted L^p estimates for the Bergman and Szegő projections on strongly pseudoconvex domains with near minimal smoothness

Nathan A. Wagner
, Brett D. Wick

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove the weighted L^p regularity of the ordinary Bergman and Cauchy-Szegő projections on strongly pseudoconvex domains D in Cⁿ with near minimal smoothness for appropriate generalizations of the B_p/A_p classes. In particular, the B_p/A_p Muckenhoupt type condition is expressed relative to balls in a quasi-metric that arises as a space of homogeneous type on either the interior or the boundary of the domain D.

Original language	English
Article number	107745
Journal	Advances in Mathematics
Volume	384
DOIs	https://doi.org/10.1016/j.aim.2021.107745
State	Published - Jun 25 2021

Keywords

Bergman projection
Békollè-Bonami
Muckenhoupt
Strongly pseudoconvex
Szegő projection

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10.1016/j.aim.2021.107745

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title = "Weighted Lp estimates for the Bergman and Szeg{\H o} projections on strongly pseudoconvex domains with near minimal smoothness",

abstract = "We prove the weighted Lp regularity of the ordinary Bergman and Cauchy-Szeg{\H o} projections on strongly pseudoconvex domains D in Cn with near minimal smoothness for appropriate generalizations of the Bp/Ap classes. In particular, the Bp/Ap Muckenhoupt type condition is expressed relative to balls in a quasi-metric that arises as a space of homogeneous type on either the interior or the boundary of the domain D.",

keywords = "Bergman projection, B{\'e}koll{\`e}-Bonami, Muckenhoupt, Strongly pseudoconvex, Szeg{\H o} projection",

author = "Wagner, \{Nathan A.\} and Wick, \{Brett D.\}",

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year = "2021",

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doi = "10.1016/j.aim.2021.107745",

language = "English",

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TY - JOUR

T1 - Weighted Lp estimates for the Bergman and Szegő projections on strongly pseudoconvex domains with near minimal smoothness

AU - Wagner, Nathan A.

AU - Wick, Brett D.

PY - 2021/6/25

Y1 - 2021/6/25

N2 - We prove the weighted Lp regularity of the ordinary Bergman and Cauchy-Szegő projections on strongly pseudoconvex domains D in Cn with near minimal smoothness for appropriate generalizations of the Bp/Ap classes. In particular, the Bp/Ap Muckenhoupt type condition is expressed relative to balls in a quasi-metric that arises as a space of homogeneous type on either the interior or the boundary of the domain D.

AB - We prove the weighted Lp regularity of the ordinary Bergman and Cauchy-Szegő projections on strongly pseudoconvex domains D in Cn with near minimal smoothness for appropriate generalizations of the Bp/Ap classes. In particular, the Bp/Ap Muckenhoupt type condition is expressed relative to balls in a quasi-metric that arises as a space of homogeneous type on either the interior or the boundary of the domain D.

KW - Bergman projection

KW - Békollè-Bonami

KW - Muckenhoupt

KW - Strongly pseudoconvex

KW - Szegő projection

UR - https://www.scopus.com/pages/publications/85104712001

U2 - 10.1016/j.aim.2021.107745

DO - 10.1016/j.aim.2021.107745

M3 - Article

AN - SCOPUS:85104712001

SN - 0001-8708

VL - 384

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 107745

ER -

Weighted L^p estimates for the Bergman and Szegő projections on strongly pseudoconvex domains with near minimal smoothness

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Keywords

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