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MiS Preprint

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces

Piotr Hajlasz and Pawel Strzelecki


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.


Related publications

1998 Repository Open Access
Piotr Hajlasz and Pawel Strzelecki

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces

In: Mathematische Annalen, 312 (1998) 2, pp. 341-362