Real-variable characterizations of local Hardy spaces on spaces of homogeneous type
Real-variable characterizations of local Hardy spaces on spaces of homogeneous type
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齐次类型空间上局部 Hardy 空间的实变量表征
DOI：
10.1002/mana.201900320
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发表时间：
2021
影响因子：
1
通讯作者：
Yuan Wen
中科院分区：
文献类型：
--
作者：
He Ziyi;Yang Dachun;Yuan Wen
设R. R. Coifman和G.韦斯意义下的齐型空间，上维数为μ。设η为P. Auscher和T.海托宁本文通过局部巨极大函数引入了局部哈代空间，并通过局部径向极大函数、局部非切极大函数、局部原子和局部Littlewood-Paley函数刻画了局部Hardy空间.进一步建立了整体与局部哈代空间之间的关系。最后，作者还得到了的有限原子特征。作为应用，给出了当的对偶空间，进一步完善了G. Dafni和H.月上双空。本文还回答了R. R. Coifman和G.韦斯的任何额外的几何假设的不必要性，除了双重条件的径向极大函数表征时。
Letbe a space of homogeneous type, with upper dimension μ, in the sense of R. R. Coifman and G. Weiss. Let η be the Hölder regularity index of wavelets constructed by P. Auscher and T. Hytönen. In this article, the authors introduce the local Hardy spacevia local grand maximal functions and also characterizevia local radial maximal functions, local non‐tangential maximal functions, local atoms and local Littlewood–Paley functions. Furthermore, the authors establish the relationship between the global and the local Hardy spaces. Finally, the authors also obtain the finite atomic characterizations of. As an application, the authors give the dual spaces ofwhen, which further completes the result of G. Dafni and H. Yue on the dual space of. This article also answers the question of R. R. Coifman and G. Weiss on the nonnecessity of any additional geometric assumptions except the doubling condition for the radial maximal function characterization ofwhen.