Abstract
We consider an abstract CR manifold equipped with a strictly positive definite Levi form, which defines a pseudo-Hermitian metric on the manifold. On such a manifold it is possible to define a natural sums of squares sub-Laplacian operator. We use Bochner identities to obtain Cordes–Friedrichs type inequalities on such manifolds where the L 2 norm of the Hessian tensor of a function is controlled by the L 2 norm of the sub-Laplacian of the function with a sharp constant for the inequality. By perturbation we proceed to develop a Cordes–Nirenberg type theory for non-divergence form equations on CR manifolds. Some applications are given to the regularity of p-Laplacians on CR manifolds.
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Chanillo, S., Manfredi, J.J. (2010). Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds. In: Cabrelli, C., Torrea, J. (eds) Recent Developments in Real and Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4588-5_8
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DOI: https://doi.org/10.1007/978-0-8176-4588-5_8
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