Abstract
This chapter is mainly devoted to the study of the local version of H 1(μ) and its dual space. First, we introduce a local atomic Hardy space h 1(μ) and a local BMO-type space rbmo (μ). After presenting some basic properties of these spaces, we then prove that the space rbmo (μ) satisfies the John–Nirenberg inequality and its predual space is h 1(μ). Moreover, we also establish the relations between H 1(μ) and h 1(μ) as well as between RBMO (μ) and rbmo (μ). In addition, we also introduce a BLO-type space RBLO (μ) and its local version rblo (μ) on \(({\mathbb{R}}^{D},\vert \cdot \vert,\mu )\) with μ as in (0.0.1) and establish some characterizations of both RBLO (μ) and rblo (μ).
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Yang, D., Yang, D., Hu, G. (2013). The Local Atomic Hardy Space h 1(μ). In: The Hardy Space H1 with Non-doubling Measures and Their Applications. Lecture Notes in Mathematics, vol 2084. Springer, Cham. https://doi.org/10.1007/978-3-319-00825-7_4
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DOI: https://doi.org/10.1007/978-3-319-00825-7_4
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Online ISBN: 978-3-319-00825-7
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