TitoloThe sharp maximal function approach to L^p estimates for operators structured on Hörmander's vector fields
Autore/iBramanti, M.; Toschi, M.
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AbstractWe consider a nonvariational degenerate elliptic operator structured on a system of left invariant, 1-homogeneous, Hörmander'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 Bramanti-Brandolini in [Rend. Sem. Mat. dell'Univ. e del Politec. di Torino, Vol. 58, 4 (2000), 389-433], extending to this context Krylov' technique, introduced in [Comm. in P.D.E.s, 32 (2007), 453-475], consisting in estimating the sharp maximal function of the second order derivatives.