Uniform Boundedness for Approximations of the Identity with Nondoubling Measures
Uniform Boundedness for Approximations of the Identity with Nondoubling Measures
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DOI：
10.1155/2007/19574
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发表时间：
2007-10
影响因子：
1.6
通讯作者：
Dachun Yang;Dongyong Yang
中科院分区：
文献类型：
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作者：
Dachun Yang;Dongyong Yang
设为非负Radon测度，满足增长条件，存在常数且使得对所有和，，其中是中心为且半径为的开球。在哈代空间和BLO-型空间RBLO中，证明了Tolsa引入的恒等式的逼近的一致有界性.此外，作者还引入了与该恒等式的一个给定逼近相关联的极大算子（齐次）和（非齐次），并证明了从到有界和从局部原子哈代空间到有界.这些结果对于建立和、BMO型空间RBMO与rbmo、RBLO与rblo之间的关系以及刻画rbmo与rblo具有重要意义.
Let be a nonnegative Radon measure on which satisfies the growth condition that there exist constants and such that for all and,, where is the open ball centered at and having radius. In this paper, the authors establish the uniform boundedness for approximations of the identity introduced by Tolsa in the Hardy space and the BLO-type space RBLO. Moreover, the authors also introduce maximal operators (homogeneous) and (inhomogeneous) associated with a given approximation of the identity, and prove that is bounded from to and is bounded from the local atomic Hardy space to. These results are proved to play key roles in establishing relations between and, BMO-type spaces RBMO and rbmo as well as RBLO and rblo, and also in characterizing rbmo and rblo.