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

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

2009-10-15

arxiv.org/abs/0910.2895v2

Mathematics

Differential Geometry

Scientific paper

Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold
with a doubling measure are considered. Under the assumption of a Poincar\'e
inequality, the space $\Mone$, defined by Haj{\l}asz, 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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