流形上Hajerasz索伯列夫空间$\Mone$的原子分解
An atomic decomposition of the Hajłasz Sobolev space $\Mone$ on manifolds
摘要：
考虑了具有加倍测度的黎曼流形上索伯列夫空间的几种可能的概念.在Poincaré不等式的假设下，Hajerasz定义的空间$\Mone$等同于用原子定义的Hardy-索伯列夫空间.在齐性空间和非齐性空间中证明了分解结果。
英文摘要：
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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