Gaussian Estimates for Second-Order Operators with Unbounded Coefficients

We study second-order differential operators A with lower-order coefficients in some Lq L . We prove the generation of positive, quasi-contractive C0 semigroups on Lp for all p Ž1, .. If the second-order coefficients are in some Lq L , we get upper pseudo-Gaussian bounds of the heat kernel. Maximal regularity, spectral independence on Lp, and analyticity of the generated semigroup on L1 are studied for these operators