OUHABAZ, El Maati; A. F. M. TER ELST, .

doi:10.2422/2036-2145.201201_005

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OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

A. F. M. TER ELST, .
University of Auckland [Auckland]

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Ce document a été publié dans

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. 2015, vol. XIV, n° 1, p. 37-81

Scuola Normale Superiore

Résumé en anglais

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.< Réduire