Partial Gaussian bounds for degenerate operators II

Let A = P @k ckl @l be a degenerate sectorial di erential operator with complex bounded mesaurable coe cients. Let Rd be open and suppose that A is strongly elliptic on . Further, let 2 C1 b (Rd) be such that an "-neighbourhood of supp is contained in . Let 2 (0; 1] and suppose that the cklj 2 C0; ( ). Then we prove (Holder) Gaussian kernel bounds for the kernel of the operator u 7! St( u), where S is the semigroup generated by A. Moreover, if = 1 and the coe cients are real, then we prove Gaussian bounds for the kernel of the operator u 7! Stu and for the derivatives in the rst variable. Finally we show boundedness on Lp(Rd) of restricted Riesz transforms.Aux frontières de l'analyse Harmoniqu