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| New Molecular Characterization of Musielak-Orlicz Hardy Spaces on Spaces of Homogeneous Type and Its Applications |
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Citation： |
Xianjie YAN,Dachun YANG.New Molecular Characterization of Musielak-Orlicz Hardy Spaces on Spaces of Homogeneous Type and Its Applications[J].Chinese Annals of Mathematics B,2025,46(2):201~232 |
| Page view： 453
Net amount： 254 |
Authors： |
Xianjie YAN; Dachun YANG |
Foundation： |
the National Key Research and Development Program of China
(No. 2020YFA0712900), the National Natural Science Foundation of China (Nos. 12301112, 12371093,
12431006) and China Postdoctoral Science Foundation (No. 2022M721024). |
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| Abstract： |
Let (X , d, μ) be a space of homogeneous type, in the sense of Coifman and
Weiss, and ? : X × [0, ∞) → [0, ∞) satisfy that, for almost every x ∈ X , ?(x, ·) is an
Orlicz function and that ?(·, t) is a Muckenhoupt A∞(X ) weight uniformly in t ∈ [0, ∞).
In this article, the authors first establish a new molecular characterization, associated
with admissible sequences of balls on X , of the Musielak-Orlicz Hardy space H ?(X ). As
an application, the authors also obtain the boundedness of Calder′on-Zygmund operators
from H ?(X ) to H ?(X ) or to the Musielak-Orlicz space L?(X ). The main novelty of these
results is that, in the proof of the boundedness of Calder′on-Zygmund operators on H ?(X ),
the authors get rid of the dependence on the reverse doubling property of μ by using this
new molecular characterization of H ?(X ) |
Keywords： |
Space of homogeneous type Musielak-Orlicz function Hardy space,
Molecule Calder´on-Zygmund operator |
Classification： |
46E36, 42B30, 42B20, 42B35, 30L99 |
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