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2013 ESTIMATES FOR $\bar\partial$ AND HANKEL OPERATORS ON GENERALIZED FOCK SPACES ON ${\mathbb C}^n$
Hong Rae Cho
Taiwanese J. Math. 17(4): 1197-1210 (2013). DOI: 10.11650/tjm.17.2013.2027

Abstract

Let $\varphi: \mathbb{C}^n \to\mathbb{R}$ be a $C^2$ plurisubharmonic function on $\mathbb{C}^n$. Suppose that there exist $C_1, C_2 \gt 0$ such that $\sup_{\mathbb{C}^n} |\bar\partial \partial\varphi| \lt C_1$ and $H_{\varphi}(\xi,\xi)(z) \geq C_2 |\xi|^2$ for $\xi \in \mathbb{R}^{2n}$ and $z \in \mathbb{C}^n$, where $H_{\varphi}(\xi,\xi)(z)$ is the real Hessian of $\varphi$ at $z$. We prove $L^{p, \varphi}$ estimates for $\bar\partial$ on $\mathbb{C}^n$ for all $p \in [1,\infty]$. Moreover, by using the estimates for $\bar\partial$, we characterize boundedness and compactness of Hankel operators with anti-holomorphic symbols on generalized Fock spaces on $\mathbb{C}^n$.

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Hong Rae Cho. "ESTIMATES FOR $\bar\partial$ AND HANKEL OPERATORS ON GENERALIZED FOCK SPACES ON ${\mathbb C}^n$." Taiwanese J. Math. 17 (4) 1197 - 1210, 2013. https://doi.org/10.11650/tjm.17.2013.2027

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1277.32004
MathSciNet: MR3085506
Digital Object Identifier: 10.11650/tjm.17.2013.2027

Subjects:
Primary: 32W05
Secondary: 47B35

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 4 • 2013
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