The Formula for the Quasicentral Modulus in the Case of Spectral Measures on Fractals

We prove a general ampliation homogeneity result for the quasicentral modulus of an n-tuple of operators with respect to the (p,1) Lorentz normed ideal. We use this to prove a formula involving Hausdorff measure for the quasicentral modulus of n-tuples of commuting Hermitian operators the spectrum of which is contained in certain Cantor-like self-similar fractals.