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Along the line of singular value estimates for commutators byRochberg-Semmes, Lord-McDonald-Sukochev-Zanin and Fan-Lacey-Li, we establishthe endpoint weak Schatten class estimate for commutators of Riesz transformswith multiplication operator $M_f$ on Heisenberg groups via homogeneous Sobolevnorm of the symbol $f$. The new tool we exploit is the construction of asingular trace formula on Heisenberg groups, which, together with the use ofdouble operator integrals, allows us to bypass the use of Fourier analysis andprovides a solid foundation to investigate the singular values estimates forsimilar commutators in general stratified Lie groups.

Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups