Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications

2018/04/04 by Bui, The Anh, Duong, Xuan Thinh, Ly, Fu Ken · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.01347

Abstract

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.

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• Robin Problems of Elliptic Equations on Rough Domains: Hölder Regularity, Green's Functions, and Harmonic Measures
• On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator

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