For Bessel-Riesz commutators on R^{n+1}_+, the singular values obey lim t^{1/(n+1)} mu(t,[M_f,R_{lambda,k}]) = C ||f||_{W-dot}^{1,n+1}, and the endpoint weak Schatten norm is equivalent to the same Sobolev norm.
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Spectral asymptotic formula of Bessel--Riesz commutator
For Bessel-Riesz commutators on R^{n+1}_+, the singular values obey lim t^{1/(n+1)} mu(t,[M_f,R_{lambda,k}]) = C ||f||_{W-dot}^{1,n+1}, and the endpoint weak Schatten norm is equivalent to the same Sobolev norm.