The sharp maximal function approach to L^p estimates for operators\n structured on H "ormander's vector fields

2015/11/11 by Marco Bramanti, Bramanti, Marco, Marisa Toschi +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1511.03536

openalex publication_date 2015/11/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider a nonvariational degenerate elliptic operator structured on a\nsystem of left invariant, 1-homogeneous, H "ormander's vector fields on a\nCarnot group in Rⁿ, where the matrix of coefficients is symmetric,\nuniformly positive on a bounded domain of Rⁿ and the coefficients are\nbounded, measurable and locally VMO in the domain. We give a new proof of the\ninterior L^p estimates on the second order derivatives with respect to the\nvector fields, first proved by Bramanti-Brandolini in [Rend. Sem. Mat.\ndell'Univ. e del Politec. di Torino, Vol. 58, 4 (2000), 389-433], extending to\nthis context Krylov' technique, introduced in [Comm. in P.D.E.s, 32 (2007),\n453-475], consisting in estimating the sharp maximal function of the second\norder derivatives.\n

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