New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications
New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications
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DOI：
10.1002/cpa.20080
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发表时间：
2005-10
影响因子：
3
通讯作者：
X. Duong;Lixin Yan
中科院分区：
文献类型：
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作者：
X. Duong;Lixin Yan
本文在齐型空间或齐型空间的可测子集上引入并发展了一些新的BMO(有界平均振荡)型函数空间。新的函数空间是由与恒等式的广义逼近相关的极大函数的变体定义的，它们推广了经典的BMO空间。我们证明了John-Nirenberg不等式在这些空间上成立，并且它们用复插值方法对Lp空间进行插补。然后，我们给出了核不满足Hörmander条件的奇异积分的Lp有界性的应用。©2005威利期刊公司。
In this paper, we introduce and develop some new function spaces of BMO (bounded mean oscillation) type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type. The new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity, and they generalize the classical BMO space. We show that the John‐Nirenberg inequality holds on these spaces and they interpolate with Lp spaces by the complex interpolation method. We then give applications on Lp‐boundedness of singular integrals whose kernels do not satisfy the Hörmander condition. © 2005 Wiley Periodicals, Inc.