Abstract
The theory of Hardy spaces over \({\mathbb {R}}^n\), originated by C. Fefferman and Stein [1], was generalized several decades ago to the case of subsets of \({\mathbb {R}}^n\). The pioneering work of generalization was done by Jonsson, Sjögren, and Wallin [2] for the case of suitable closed subsets and by Miyachi [3] for the case of proper open subsets. In this article, we study Hardy spaces on proper open \(\Omega \subset \mathbb {R}^n\), where \(\Omega \) satisfies a doubling condition and \(|\Omega |=\infty \). We first establish a variant of the Calderón–Zygmund decomposition, and then explore the relationship among Hardy spaces by means of atomic decomposition, radial maximal function, and grand maximal function.
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The authors would like to express their deep gratitude to referees for their very careful reading, valuable comments, and helpful suggestions, which made the paper more accurate and readable.
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The authors were supported by National Science and Technology Council, R.O.C. under grant numbers #NSTC 112-2115-M-008-001-MY2, #MOST 109-2115-M-008-002-MY3, and #MOST 110-2811-M-008-517, respectively, as well as supported by National Center for Theoretical Sciences of R.O.C.
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Lee, MY., Lin, CC. & Ooi, K.H. Hardy Spaces on Open Subsets of \(\mathbb {R}^n\). J Geom Anal 34, 20 (2024). https://doi.org/10.1007/s12220-023-01468-7
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DOI: https://doi.org/10.1007/s12220-023-01468-7