trace and the non-separability of its domain of definition makes computations and estimates of Dixmier traces a challenging problem. In this paper we propose a methodology to estimate Dixmier traces of powers of Hankel operators, building on work of Gayral-Sukochev [@GS].

The inspiration for this work is a paper by Engliš-Zhang [@EZ] where Dixmier traces of Hankel operators in the Lorentz ideal $\mathcal{M}_{1,\infty}$ were estimated by means of Besov norms. Recent work in fractal geometry [@juliaconnes; @quasiconnes] and the questions posed in [@EZ Section 7.3] lead us to ask for an extension of the estimates in [@EZ] to powers $p\geq 1$ and more general Lorentz ideals. The approach we take in this paper differs from that of [@EZ]. Our method consists of a rather straightforward application of extrapolation results of Gayral-Sukochev [@GS].

In the classical examples, naturally appearing physical and geometrical operators are measurable, that is all Dixmier traces take the same value on such operators. An example of a non-measurable pseudo-differential operator with symbol of Hörmander type $(1,0)$ can be found in [@LSZ Proposition 11.3.22]. Engliš-Zhang [@EZ Theorem 4] constructed a non-measurable Hankel operator from $\mathcal{M}_{1,\infty}$. We show that there are non-measurable Hankel operators in any ($p$-convexified) Lorentz ideal.

