Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}$$\end{document} Estimates for the Bergman Projection on Generalized Fock Spaces

被引：0
作者：
Thuc Trong Phung
机构：
[1] Faculty of Applied Science-Ho Chi Minh City University of Technology (HCMUT),
[2] Vietnam National University Ho Chi Minh City,undefined
来源：
The Journal of Geometric Analysis | 2024年 / 34卷 / 6期
关键词：
Bergman projection; regularity; -operator; Fock space; Primary 32A25; Secondary 32A36;
D O I：
10.1007/s12220-024-01618-5
中图分类号：
学科分类号：
摘要：
We obtain Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p}$$\end{document} bounds for the Bergman projection Pφ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{\varphi }$$\end{document} on Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^{n}$$\end{document} for a class of weights φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} whose complex Hessian has comparable eigenvalues. This relies on an extension of the estimate on the Bergman kernel obtained previously by Dall’Ara.
引用
收藏
相关论文
共 18 条
[1]  
Azagra D(2007)Smooth approximation of Lipschitz functions on Riemannian manifolds J. Math. Anal. Appl. 326 1370-1378
[2]  
Ferrera J(2016)Parameter dependence of the Bergman kernels Adv. Math. 299 108-138
[3]  
López-Mesas F(1991)On the $\overline{\partial }$ equation in weighted $L^2$ norms in ${ C}^1$ J. Geom. Anal. 1 193-230
[4]  
Rangel Y(2015)Pointwise estimates of weighted Bergman kernels in several complex variables Adv. Math. 285 1706-1740
[5]  
Chen B-Y(1998)Pointwise estimates for the weighted Bergman projection kernel in ${ {C}}^n$, using a weighted $L^2$ estimate for the $\overline{\partial }$ equation Ann. Inst. Fourier (Grenoble) 48 967-997
[6]  
Christ M(2007)Compactness of the solution operator to $\overline{\partial }$ in weighted $L^2$-spaces J. Funct. Anal. 243 679-697
[7]  
Dall’Ara GM(2003)Interpolating and sampling sequences for entire functions Geom. Funct. Anal. 13 862-914
[8]  
Delin H(2009)Pointwise estimates for the Bergman kernel of the weighted Fock space J. Geom. Anal. 19 890-910
[9]  
Haslinger F(2001)Sampling in weighted $L^p$ spaces of entire functions in ${\mathbb{C} }^n$ and estimates of the Bergman kernel J. Funct. Anal. 182 390-426
[10]  
Helffer B(1995)$L^p$ estimates for Schrödinger operators with certain potentials Ann. Inst. Fourier (Grenoble) 45 513-546
12