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Abstract
The theory of Hardy spaces over Rn , originated by C. Fefferman and Stein [1], was generalized several decades ago to the case of subsets of Rn . 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 Ω ⊂ Rn , where Ω satisfies a doubling condition and | Ω | = ∞ . 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.
Original language | English |
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Article number | 20 |
Journal | Journal of Geometric Analysis |
Volume | 34 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2024 |
Keywords
- Calderón–Zygmund decomposition
- Hardy spaces
- Maximal functions
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