Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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REAL-VARIABLE CHARACTERIZATIONS OF VARIABLE HARDY SPACES ON LIPSCHITZ DOMAINS OF ℝn

  • Liu, Xiong (School of Mathematics and Statistics Lanzhou University)
  • Received : 2020.06.22
  • Accepted : 2020.11.18
  • Published : 2021.05.31
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Abstract

Let Ω be a proper open subset of ℝn and p(·) : Ω → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the author introduces the "geometrical" variable Hardy spaces Hp(·)r (Ω) and Hp(·)z (Ω) on Ω, and then obtains the grand maximal function characterizations of Hp(·)r (Ω) and Hp(·)z (Ω) when Ω is a strongly Lipschitz domain of ℝn. Moreover, the author further introduces the "geometrical" variable local Hardy spaces hp(·)r (Ω), and then establishes the atomic characterization of hp(·)r (Ω) when Ω is a bounded Lipschitz domain of ℝn.

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Acknowledgement

The author would like to express his deep thanks to the referee for his very careful reading and useful comments which do improve the presentation of this article. The author is very grateful to Professor Sibei Yang for his guidance.

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