Levi's parametrix for some sub-elliptic non-divergence form operators.
We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the -harmonic extensions of VMO vector-valued functions. The operators we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity...
We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
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