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Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications. (English) Zbl 1430.42024

Summary: 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, Schrödinger operators with Dirichlet boundary conditions, and Fourier-Bessel operators.

MSC:

42B30 \(H^p\)-spaces
42B35 Function spaces arising in harmonic analysis
35K08 Heat kernel
35J25 Boundary value problems for second-order elliptic equations
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