Open AccessPartial Gaussian bounds for degenerate differential operators II
Author(s) -
A. F. M. ter Elst,
El Maati Ouhabaz
Publication year - 2015
Publication title -
annali della scuola normale superiore di pisa. classe di scienze
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.444
H-Index - 37
eISSN - 2036-2145
pISSN - 0391-173X
DOI - 10.2422/2036-2145.201201_005
Subject(s) - mathematics , semigroup , degenerate energy levels , gaussian , operator (biology) , differential operator , kernel (algebra) , elliptic operator , pure mathematics , combinatorics , hypoelliptic operator , discrete mathematics , semi elliptic operator , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
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