ON THE DOMAINS OF ELLIPTIC OPERATORS IN L1

We prove optimal embedding estimates for the domains of second-order elliptic operators in L-1 spaces. Our procedure relies on general semigroup theory and interpolation arguments, and on estimates for del T(t)f in L-1, in L-infinity, and possibly in fractional Sobolev spaces, for f is an element of L-1. It is applied to a number of examples, including some degenerate hypoelliptic operators, and operators with unbounded coefficients.