Partial Gaussian bounds for degenerate differential operators II

• A.F.M. ter Elst ^[1] ; El Maati Ouhabaz ^[2]
  1. [1] University of Auckland

     University of Auckland

     Nueva Zelanda

     
  2. [2] Univ. Bordeaux, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 1, 2015, págs. 37-81
• Idioma: inglés
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• Resumen

  • Let A = − P @k ckl @l be a degenerate sectorial differential operator with complex boundedmesaurable coefficients. Let ⇢ Rd be open and suppose that A is strongly elliptic on . Further, let # 2 C1b (Rd ) be such that an "- neighbourhood of supp # is contained in . Let ⌫ 2 (0, 1] and suppose that the ckl | 2 C0,⌫ (). Then we prove (H¨older) 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 coefficients are real, then we prove Gaussian bounds for the kernel of the operator u 7!# St u and for the derivatives in the first variable. Finally we show boundedness on L p(Rd ) of restricted Riesz transforms.