Commutators of Hilbert transforms along monomial curves

The Hilbert transforms associated with monomial curves have a natural non-isotropic structure. We study the commutator of such and symbol $b$ prove upper bound this when is in corresponding BMO space by using Cauchy integral trick. also consider lower introducing new testing given curve, which shows that classical contained space. show non-zero curvature are important, since considering lines, parallel version overlaps but do not containment.