Codice  QDD215 
Titolo  The sharp maximal function approach to L^p estimates for operators structured on HÃ¶rmander's vector fields 
Data  20151111 
Autore/i  Bramanti, M.; Toschi, M. 
Link  Download full text 
Abstract  We consider a nonvariational degenerate elliptic operator structured on a system of left invariant, 1homogeneous, HÃ¶rmander's vector fields on a Carnot group in R^n, where the matrix of coefficients is symmetric, uniformly positive on a bounded domain of R^n and the coefficients are bounded, measurable and locally VMO in the domain. We give a new proof of the interior L^p estimates on the second order derivatives with respect to the vector fields, first proved by BramantiBrandolini in [Rend. Sem. Mat. dell'Univ. e del Politec. di Torino, Vol. 58, 4 (2000), 389433], extending to this context Krylov' technique, introduced in [Comm. in P.D.E.s, 32 (2007), 453475], consisting in estimating the sharp maximal function of the second order derivatives. 
