An atomic decomposition of the Hajlasz Sobolev space M-1(1) on manifolds

作者：Badr N; Dafni G^*

来源：Journal of Functional Analysis, 2010, 259(6): 1380-1420.

DOI：10.1016/j.jfa.2010.05.020

• Hardy-Sobolev spaces
• Atomic decomposition
• Metric measure spaces
• Hajlasz-Sobolev spaces

Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption-of a Poincare inequality, the space M-1(1), defined by Hajlasz, is identified with a Hardy-Sobolev space defined in terms of atoms. Decomposition results are proved for both the homogeneous and the nonhomogeneous spaces.

• 出版日期2010-9-15