Geodesic
Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 207-217.

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On complete pseudoconvex Reinhardt domains in $\mathbb {C}^2$, we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in $\mathbb {C}^2$ that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite dimensional and the Hankel operator $H_{\bar {z}_1 \bar {z}_2}$ is Hilbert-Schmidt.
DOI : 10.21136/CMJ.2017.0471-15
Classification : 32A36, 47B10, 47B35
Keywords: canonical solution operator for $\overline {\partial }$-problem; Hankel operator; Hilbert-Schmidt operator 
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Çelik, Mehmet; Zeytuncu, Yunus E. Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 207-217. doi : 10.21136/CMJ.2017.0471-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0471-15/

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