Abstract
We give a complete characterization of Schatten class Hankel operatorsHfH_facting on weighted Segal-Bargmann spacesF2(φ)F^2(\varphi )using the notion of integral distance to analytic functions inCn\mathbb {C}^nand Hörmander’s∂¯\bar \partial-theory. Using our characterization, forf∈L∞f\in L^\inftyand1>p>∞1>p>\infty, we prove thatHfH_fis in the Schatten classSpS_pif and only ifHf¯∈SpH_{\bar {f}}\in S_p, which was previously known only for the Hilbert-Schmidt classS2S_2of the standard Segal-Bargmann spaceF2(φ)F^2(\varphi )withφ(z)=α|z|2\varphi (z) = \alpha |z|^2.
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