θ-型Calderón-Zygmund算子与Lipschitz函数生成的交换子的有界性
Boundedness of Commutators with θ-Type Calderón-Zygmund Operators and Lipschitz Function
DOI: 10.12677/PM.2022.121008, PDF,  被引量    科研立项经费支持
作者: 朱晓矇：牡丹江师范学院，黑龙江 牡丹江
关键词: θ-型Calderón-Zygmund算子；交换子；Lipschitz空间；Campanato空间；θ-Type Calderón-Zygmund Operators； Commutators； Lipschitz Spaces； Campanato Spaces
摘要: 本文研究了θ-型Calderón-Zygmund算子与Lipschitz函数b∈Λγ·(Rn)生成的交换子，当θ满足一类Dini条件时，证明了交换子在γ=β+n/p时是从Lebesgue空间Lp(Rn)到Campanato空间Cp,β(Rn)有界的。
Abstract: In this paper, we consider the boundedness of commutators with θ-type Calderón-Zygmund Operators and Lipschitz Function b∈Λγ·(Rn). When θ satisfies a class of Dini type conditions, it is proved that commutators are bounded from Lebesgue spaces Lp(Rn) to Campanato spaces Cp,β(Rn) when γ=β+n/p.
文章引用：朱晓矇. θ-型Calderón-Zygmund算子与Lipschitz函数生成的交换子的有界性[J]. 理论数学, 2022, 12(1): 54-61. https://doi.org/10.12677/PM.2022.121008

参考文献

[1] Coifman, R.R., Rochberg, R. and Weiss, G. (1976) Factorization Theorems for Hardy Spaces in Several Variables. Annals of Mathematics, 103, 611-635. [Google Scholar] [CrossRef] 
[2] Pérez, C. (1995) Endpoint Estimates for Commutators of Singular Integral Operators. Journal of Functional Analysis, 128, 163-185. [Google Scholar] [CrossRef] 
[3] Janson, S. (1978) Mean Oscillation and Commutators of Singular In-tegral Operators. Arkiv för Matematik, 16, 263-270. [Google Scholar] [CrossRef] 
[4] Paluszyński, M. (1995) Characterization of the Besove Spaces via the Commutator Operator of Coifman Rochberg and Weiss. Indiana University Mathematics Journal, 44, 1-17. [Google Scholar] [CrossRef] 
[5] Zhang, L., Shi, S.G. and Huang, H. (2015) New Characterizations of Lipschitz Space via Commutors on Morrey Spaces. Advances in Mathematics (China), 44, 899-907.
[6] Yabuta, K. (1985) Generalizations of Calderón-Zygmund Operators. Studia Mathematica, 82, 17-31. [Google Scholar] [CrossRef] 
[7] Coifman, R.R. and Meyer, Y. (1978) Au-delà des opérateurs pseu-do-différentiels. Astérisque. Soc. Math. France, Paris.
[8] Liu, Z.G. and Lu, S.Z. (2002) Endpoint Estimates for Commutators of Calderón-Zygmund Type Operators. Kodai Mathematical Journal, 25, 79-88. [Google Scholar] [CrossRef] 
[9] 张璞, 徐罕. Calderón-Zygmund型算子交换子的加权尖锐估计[J]. 数学学报, 2005, 48(4): 625-636.
[10] 程美芳, 束立生. 型Calderón-Zygmund奇异积分算子交换子在Triebel-Lizorkin空间上的有界性[J]. 数学研究, 2006, 39(4): 375-378.
[11] DeVore, R.A. and Sharpley, R.C. (1984) Maximal Functions Measuring Smoothness. Memoirs of the American Mathematical Society, 47, 4-113. [Google Scholar] [CrossRef] 

为你推荐