| 王艳,刘宗光,于夏.多线性 Dunkl 奇异积分交换子的有界性[J].数学年刊A辑,2025,46(3):247~264 |
| 多线性 Dunkl 奇异积分交换子的有界性 |
| Boundedness of Commutators of Multilinear Singular Integrals in the Dunkl Setting |
| Received:March 19, 2025 Revised:September 19, 2025 |
| DOI：10.16205/j.cnki.cama.2025.0015 |
| 中文关键词: Dunkl 算子，Lipschitz 空间，交换子 |
| 英文关键词:Dunkl setting, Lipschitz space, Commutator |
| 基金项目: |
| Author Name | Affiliation | | WANG Yan、 | 1 School of Science, China University of Mining and Technology, Beijing 100083, China； | | LIU Zongguang、 | 1 School of Science, China University of Mining and Technology, Beijing 100083, China； | | YU Xia | 2 School of Mathematics and Information Sciences, Yantai University, Yantai 264005, Shandong, China |
|
| Hits: 138 |
| Download times: 386 |
| 中文摘要: |
| 研究了 Lipschitz 函数与 Dunkl 型奇异积分算子生成的两类多线性交换子的有界性，证明了交换子在乘积加权 Lebesgue 空间
L
p
1
?
(R
N
,?dμ
κ
?
)×?×L
p
m
?
(R
N
,?dμ
κ
?
)
到 Dunkl 型 Triebel-Lizorkin 空间
F
˙
p,D
β,∞
?
(R
N
)
的有界性，进一步地，通过引入 sharp 极大函数估计，建立了其从上述乘积空间到加权 Lebesgue 空间
L
q
(R
N
,?dμ
κ
?
)
的有界性。 |
| 英文摘要: |
| In this paper, the authors study the boundedness of two classes of multilinear commutators generated by Lipschitz functions and singular integral operators in the Dunkl setting. First, the authors prove the boundedness of the commutators from the product weighted Lebesgue space
L
p
1
?
(R
N
,?dμ
κ
?
)×?×L
p
m
?
(R
N
,?dμ
κ
?
)
to Dunkl-type Triebel-Lizorkin space
F
˙
p,D
β,∞
?
(R
N
)
. Furthermore, by introducing sharp maximal function estimates, the authors establish the boundedness of the commutators from the same product space to weighted Lebesgue spaces
L
q
(R
N
,?dμ
κ
?
)
. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
