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In this paper we study Dixmier traces of powers of Hankel operators inLorentz ideals. We extend results of Engli\v{s}-Zhang to the case of powers$p\geq 1$ and general Lorentz ideals starting from abstract extrapolationresults of Gayral-Sukochev. In the special case $p=2,4,6$ we give an exactformula for the Dixmier trace. For general $p$, we give upper and lower boundson the Dixmier trace. We also construct, for any $p$ and any Lorentz ideal,examples of non-measurable Hankel operators.

Estimating Dixmier traces of Hankel operators in Lorentz ideals