On the parabolic Adams theorem and its applications to diffusion processes

Abstract

We show how the parabolic version of the Adams theorem and its corollary can be used to estimate in $L_{p}$ the evolution family associated to a divergence form second-order parabolic operator with parabolic Morrey lower-order terms and also how to estimate the moments of the derivatives of solutions of It\^o equations with respect to the initial data when the drift term has singularities.