Strong regularization by Brownian noise propagating through a weak Hörmander structure

We establish strong uniqueness for a class of degenerate SDEs weak Hörmander type under suitable Hölder regularity conditions the associated drift term. Our approach relies on Zvonkin transform which requires to exhibit good smoothing properties underlying parabolic PDE with rough, here Hölder, coefficients and source Such regularizing effects are established through perturbation technique (forward parametrix approach) also heavily appropriate duality Besov spaces. For method employed, we some sharp thresholds exponents hold.