Browse > Article
http://dx.doi.org/10.7858/eamj.2017.004

BERGMAN KERNEL ESTIMATES FOR GENERALIZED FOCK SPACES  

Cho, Hong Rae (Department of Mathematics, Pusan National University)
Park, Soohyun (Department of Mathematics, Pusan National University)
Publication Information
East Asian mathematical journal / v.33, no.1, 2017 , pp. 37-44 More about this Journal
Abstract
We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.
Keywords
Bergman kernel; generalized Fock space; exponential type weight;
Citations & Related Records
연도 인용수 순위
  • Reference
1 H. Arroussi and J. Pau, Reproducing kernel estimates, bounded projections and duality on large weighted Bergman spaces, J. Geom. Anal. 25 (2015), no. 4, 2284-2312.   DOI
2 S. Asserda and A. Hichame, Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights, C. R. Acad. Sci. Paris, Ser. I 352 (2014), no.1, 13-16.   DOI
3 B. Berndtsson, Weighted estimates for the ${\bar{\partial}}$-equation, in: Complex Analysis and Geometry, Columbus, OH, 1999, in: Ohio State Univ. Math. Res. Inst. Publ., 9, De Gruyter, Berlin, (2001), 43-57.
4 O. Constantin and J. A. Pelaez, Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces, J. Geom. Anal. 26 (2016), no. 2, 1109-1154.   DOI
5 M.-O. Czarnecki and L. Rifford, Approximation and regularization of Lipschitz functions: convergence of the gradients, Trans. Amer. Math. Soc., 358 (10) (2006), 4467-4520.   DOI
6 H. Delin, Pointwise estimates for the weighted Bergman projection kernel in ${\mathbb{C}}^n$ using a weighted $L^2$ estimate for the ${\bar{\partial}}$ equation, Ann. Inst. Fourier (Grenoble), 48 (4) (1998), 967-997.   DOI
7 P. Lin and R. Rochberg, Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights, Pacific J. Math. 173 (1) (1996), 127-146.   DOI
8 N. Marco, X. Massaneda and J. Ortega-Cerda, Intepolation and sampling sequence for entire functions, Geom. Funct. Anal., 13 (2003), 862-914.   DOI
9 J. Marzo and J. Ortega-Cerda, Pointwise estimates for the Bergman kernel of the weighted Fock space, J. Geom. Anal., 19 (2009), 890-910.   DOI
10 M. Pavlovic and J. A. Pelaez, An equivalence for weighted integrals of an analytic function and its derivative, Math. Nachr. 281 (2008), 1612-1623.   DOI