与广义逼近恒等式相关的弱BMO型空间
Weak BMO-Type Spaces Associated with Generalized Approximations to the Identity
DOI: 10.12677/PM.2018.83032, PDF,   
作者: 李肖杰*：北京航空航天大学，数学与系统科学学院，北京
关键词: 齐型空间；WBMOpA(χ)空间；插值；Homogeneous Space；WBMOpA(χ)Space； Interpolation
摘要: 在本篇文章中，我们引入了齐型空间χ 上与广义逼近恒等式相关的一类新的弱BMO型空间WBMOpA(χ) ，1∠p∠∞ ，它是WBMOp(χ) 空间的推广。我们证明了BMOpA(χ) 空间与WBMOpA(χ) 空间的等价性，并给出了WBMOpA(χ) 空间与LP(χ) 空间的插值定理。
Abstract: In this paper, we introduce a new weak BMO-type space WBMOpA(χ) (1∠p∠∞ )on the homogeneous space χ , which is associated with generalized approximations to the identity and generalizes WBMOp(χ) space. We show the equivalence of BMOpA(χ) space and WBMOpA(χ) space, and give the interpolation theorem of WBMOpA(χ) space and LP(χ) space.
文章引用：李肖杰. 与广义逼近恒等式相关的弱BMO型空间[J]. 理论数学, 2018, 8(3): 253-258. https://doi.org/10.12677/PM.2018.83032

参考文献

[1] John, F. and Nirenberg, L. (1961) On Function of Bounded Mean Oscillation. Communications on Pure & Applied Mathematics, 14, 415-426. [Google Scholar] [CrossRef] 
[2] Fefferman, C. and Stein, E.M. (1972) Spaces of Several Variables. Acta Mathematica, 129, 137-193. [Google Scholar] [CrossRef] 
[3] 王定怀, 周疆. 一类新型BMO空间[J]. 数学学报, 2017, 60(5): 833-846.
[4] Doung, X.T. and Yan, L.X. (2005) New Function Spaces of BMO Type, the John-Nirenberg Inequality, Interpolation, and Applications. Communications on Pure & Applied Mathematics, 58, 1375-1420. [Google Scholar] [CrossRef] 
[5] Coifman, R.R. and Weiss, G. (1977) Extensions of Hardy Spaces and Their Use in Analysis. Bulletin of the American Mathematical Society, 83, 569-645. [Google Scholar] [CrossRef] 
[6] Coifman, R.R. and Weiss, G. (1971) Analyse Hamonique Non-Commutative sur Certains Espaces Homogènes. Springer Berlin Heidelberg, 242. [Google Scholar] [CrossRef] 

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