Hardy Spaces on Open Subsets of Rn

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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 languageEnglish
Article number20
JournalJournal of Geometric Analysis
Issue number1
StatePublished - Jan 2024


  • Calderón–Zygmund decomposition
  • Hardy spaces
  • Maximal functions


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