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http://dx.doi.org/10.4134/BKMS.b200545

REAL-VARIABLE CHARACTERIZATIONS OF VARIABLE HARDY SPACES ON LIPSCHITZ DOMAINS OF ℝn  

Liu, Xiong (School of Mathematics and Statistics Lanzhou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.3, 2021 , pp. 745-765 More about this Journal
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.
Keywords
Variable Hardy space; grand maximal function; atom; Lipschitz domains;
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