Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces
Piotr Hajlasz and Pawel Strzelecki
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Submission date: 28. Nov. 1997
published in: Mathematische Annalen, 312 (1998) 2, p. 341-362
DOI number (of the published article): 10.1007/s002080050225
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We consider the regularity problem for subelliptic, sphere-valued p-harmonic maps, associated with a system of Hörmander vector fields in a bounded domain of Rn. We prove that for p equal to the homogeneous dimension Q, the maps in question are locally Hölder continuous.
Our method of proof uses an abstract lemma, which serves as a counterpart of the duality of Hardy space and BMO (even though no Hardy spaces are available in this context) and seems to be of independent interest. Its fairly simple proof, bypassing the whole burden of proof of Fefferman's duality theorem, uses just Sobolev inequality, properties of the fundamental solution of the subelliptic Laplace operator, and an abstract version of fractional integration theorem.