On the maximum principle for linear parabolic equations

We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in Lp spaces, p ≤ n to linear parabolic equations with inhomogeneous terms in Lp, p ≤ n  +  1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the positive cone . They also extend the maximum principle of Krylov for the case p  =  n + 1, corresponding to the usual parabolicity.