  In this paper, by establishing the $L^p$-$L^q$ estimate and Sobolev estimates
for parabolic partial differential equations with a singular first order term
and a Lipschitz first order term, a new Zvonkin-type transformation is given
for stochastic differential equations with singular and Lipschitz drifts. The
associated Krylov's estimate is established. As applications, Harnack
inequalities are established for stochastic equations with H\"older continuous
diffusion coefficient and singular drift term without regularity assumption.
