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On complete pseudoconvex Reinhardt domains in $\mathbb{C}^2$, we show thatthere is no nonzero Hankel operator with an anti-holomorphic symbol that isHilbert-Schmidt. We also present examples of unbounded non-pseudoconvex domainsthat admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphicsymbols.

Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains