We prove nontangential and radial maximal function characterizations for Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type with finite measure. This not only addresses an open point in the literature, but also gives a complete answer to the question posed by Coifman and Weiss in the case of finite measure. We then apply our results to give maximal function characterizations for Hardy spaces associated to second order elliptic operators with Neumann and Dirichlet boundary conditions, Schr\"odinger operators with Dirichlet boundary conditions, and Fourier--Bessel operators.

中文翻译：

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有限测度齐型空间上哈代空间的极大函数刻画及应用

我们证明了与非负自伴随算子关联的 Hardy 空间的非切向和径向最大函数表征，该算子满足对具有有限测度的齐次类型空间的高斯估计。这不仅解决了文献中的一个开放点，而且对 Coifman 和 Weiss 在有限测度情况下提出的问题给出了完整的答案。然后，我们应用我们的结果来给出与具有 Neumann 和 Dirichlet 边界条件的二阶椭圆算子、具有 Dirichlet 边界条件的 Schr\"odinger 算子和傅立叶-贝塞尔算子相关联的哈代空间的最大函数表征。