Abstract
The main purpose of this chapter is to study the Hardy space H 1(μ). To this end, we introduce the BMO-type space RBMO (μ), establish the John–Nirenberg inequality for functions in RBMO (μ) and some equivalent characterizations of RBMO (μ). We then introduce the atomic Hardy space H 1(μ) and obtain its basic properties, including that the dual space of H 1(μ) is RBMO (μ). We also characterize H 1(μ) in terms of a class of the maximal functions.
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Yang, D., Yang, D., Hu, G. (2013). The 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_3
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DOI: https://doi.org/10.1007/978-3-319-00825-7_3
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