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arXiv · 0910.2895

An atomic decomposition of the Hajłasz Sobolev space $\Mone$ on manifolds

Nadine Badr·Galia Dafni
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Abstract

Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincaré inequality, the space $\Mone$, defined by Hajłasz, is identified with a Hardy-Sobolev space defined in terms of atoms. Decomposition results are proved for both the homogeneous and the nonhomogeneous spaces.

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Nadine Badr, Galia Dafni. 2010-06-03. An atomic decomposition of the Hajłasz Sobolev space $\Mone$ on manifolds. https://arxiv.org/abs/0910.2895

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