θ-型Calderόn-Zygmund算子交换子的新加权估计

doi:10.13371/j.cnki.chin.q.j.m.2026.02.009

数学季刊 ›› 2026, Vol. 41 ›› Issue (2): 207-220.doi: 10.13371/j.cnki.chin.q.j.m.2026.02.009

• • 上一篇

θ-型Calderόn-Zygmund算子交换子的新加权估计

Department of Mathematics, Jinzhong College of Information, Jinzhong 030800, China

收稿日期:2025-06-05 出版日期:2026-06-30 发布日期:2026-06-30
作者简介:XUE Feng-yu (1997-), male, native of Datong, Shanxi, teaching assistant of Jinzhong College of Information, engages in harmonic analysis.
基金资助:
Heilongjiang Natural Science Foundation Joint Key Project (Grant No. ZL2024A001).

New Weighted Estimates for Commutators of θ-Type Calderόn-Zygmund Operator

Department of Mathematics, Jinzhong College of Information, Jinzhong 030800, China

Received:2025-06-05 Online:2026-06-30 Published:2026-06-30
About author:XUE Feng-yu (1997-), male, native of Datong, Shanxi, teaching assistant of Jinzhong College of Information, engages in harmonic analysis.
Supported by:
Heilongjiang Natural Science Foundation Joint Key Project (Grant No. ZL2024A001).

摘要/Abstract

摘要： In this paper, we investigate the boundedness of commutators generated by the θ-Calderόn-Zygmund operator with symbol function belonging to two kinds of weighted Campanato spaces. Specifically, we show that the commutators of the θ-type Calderόn-Zygmund operator are bounded from weighted Lebesgue spaces to weighted Campanato spaces when symbol function belongs to weighted Lipschitz spaces; we also show that the commutators are bounded from weighted Morrey spaces to weighted Campanato spaces when symbol function belongs to a certain weighted Campanato space.

关键词: θ-type Calder?n-Zygmund operator, Weighted Campanato space, Commutator, Weighted Morrey space

Abstract: In this paper, we investigate the boundedness of commutators generated by the θ-Calderόn-Zygmund operator with symbol function belonging to two kinds of weighted Campanato spaces. Specifically, we show that the commutators of the θ-type Calderόn-Zygmund operator are bounded from weighted Lebesgue spaces to weighted Campanato spaces when symbol function belongs to weighted Lipschitz spaces; we also show that the commutators are bounded from weighted Morrey spaces to weighted Campanato spaces when symbol function belongs to a certain weighted Campanato space.

Key words: θ-type Calder?n-Zygmund operator, Weighted Campanato space, Commutator, Weighted Morrey space

中图分类号:

O174.2

薛凤宇. θ-型Calderόn-Zygmund算子交换子的新加权估计[J]. 数学季刊, 2026, 41(2): 207-220.

XUE Feng-yu. New Weighted Estimates for Commutators of θ-Type Calderόn-Zygmund Operator[J]. Chinese Quarterly Journal of Mathematics, 2026, 41(2): 207-220.

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[2]	潘亚丽, 李昌文, 温宗良. 带变量Calderón-Zygmund核的奇异积分算子在加权Morrey空间上的有界性[J]. 数学季刊, 2015, 30(1): 39-46.
[3]	王世恒. 反对合矩阵的秩等式[J]. 数学季刊, 2013, 28(2): 311-316.
[4]	周娟, 朱月萍. 非双倍测度下多线性奇异积分算子及其交换子在Morrey-Herz型空间上的有界性[J]. 数学季刊, 2012, 27(4): 545-555.
[5]	王立伟, 束立生, 瞿萌. 有变量核的分数次积分算子交换子的CBMO估计[J]. 数学季刊, 2012, 27(1): 68-73.
[6]	刘明菊. 一类多线性算子在广义Morrey空间L^p,ω上的有界性[J]. 数学季刊, 2010, 25(4): 626-632.
[7]	朱诗红. Bochner-Riesz极大算子及交换子在广义Morrey空间中有界性[J]. 数学季刊, 2010, 25(4): 535-542.
[8]	高文华, 江寅生, 龚小兵. 齐型空间上的Herz-Morrey空间的线性交换子的有界性[J]. 数学季刊, 2010, 25(2): 172-181.
[9]	韩彦昌. 乘积空间上的Calderón-Zygmund算子嵌套交换子[J]. 数学季刊, 2007, 22(2): 187-194.
[10]	王月山, 王学敏. 类奇异积分和交换子在广义Morrey空间上的有界性[J]. 数学季刊, 2006, 21(2): 288-292.
[11]	王月山, 朱秀阁. Vilenkin群上Morrey空间里的算子有界性[J]. 数学季刊, 2003, 18(3): 315-319.
[12]	乔志军. Dirac方程族的换位表示及对合解[J]. 数学季刊, 1997, 12(1): 1-3.

θ-型Calderόn-Zygmund算子交换子的新加权估计

New Weighted Estimates for Commutators of θ-Type Calderόn-Zygmund Operator

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