Hankel Operators on Weighted Fock Spaces

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• 作者：Hélène Bommier-Hato and El Hassan Youssfi
• 关键词：Hankel operator ; Fock space ; Bergman kernel
• 刊名：Integral Equations and Operator Theory
• 出版年：2007
• 出版时间：September, 2007
• 年：2007
• 卷：59
• 期：1
• 页码：1-17
• 全文大小：333 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

We consider Hankel operators H<sub>[`(f)]</sub>H_{\bar{f}} with antiholomorphic symbol [`(f)]\bar{f} on the generalized Fock space A2(m_m){\mathcal{A}}^{2}(\mu_{m}) , where μ _m is the measure with weight e-|z|me^{{-|z|}^{m}} , m > 0 with respect to the Lebesgue measure in \mathbbCn{\mathbb{C}}^{n} . We prove that H_{[`(f)]</sub>H_{\bar{f}} is bounded if and only if f is a polynomial of degree at most \fracm2\frac{m}{2} . We show that H<sub>[`(f)]}H_{\bar{f}} is compact if and only if f is a polynomial of degree strictly smaller that \fracm2\frac{m}{2} . We also establish that H_[`(f)]H_{\bar{f}} is in the Schatten class S_p{\mathcal{S}}_{p} if and only if p > 2n and f is a polynomial of degree strictly smaller than m\frac(p-2n)2pm\frac{(p-2n)}{2p} .