Hausdorff operators on the Heisenberg group

2015 ◽  
Vol 31 (11) ◽  
pp. 1703-1714 ◽  
Author(s):  
Jiu Hua Guo ◽  
Li Jing Sun ◽  
Fa You Zhao
Keyword(s):  
Heisenberg Group ◽  
Hausdorff Operators

Weighted estimates for commutators of Hausdorff operators on the Heisenberg group

2020 ◽  
pp. 39-62
Author(s):  
Nguyen Minh Chuong ◽  
◽  
Dao Van Duong ◽  
Nguyen Duc Duyet ◽  
◽  
...  
Keyword(s):  
Heisenberg Group ◽  
Weighted Estimates ◽  
Hausdorff Operators

scholarly journals Weighted CBMO estimates for commutators of matrix Hausdorff operator on the Heisenberg group

2020 ◽  
Vol 18 (1) ◽  
pp. 496-511
Author(s):  
Amna Ajaib ◽  
Amjad Hussain
Keyword(s):  
Heisenberg Group ◽  
Herz Spaces ◽  
Hausdorff Operator ◽  
Hausdorff Operators

Abstract In this article, we study the commutators of Hausdorff operators and establish their boundedness on the weighted Herz spaces in the setting of the Heisenberg group.

Weighted Estimates for Commutators of Hausdorff Operators on the Heisenberg Group

2020 ◽  
Vol 64 (2) ◽  
pp. 35-55
Author(s):  
N. M. Chuong ◽  
D. V. Duong ◽  
N. D. Duyet
Keyword(s):  
Heisenberg Group ◽  
Weighted Estimates ◽  
Hausdorff Operators

Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group

2021 ◽  
Vol 19 (1) ◽  
pp. 316-328
Author(s):  
Yangkendi Deng ◽  
Xingsong Zhang ◽  
Dunyan Yan ◽  
Mingquan Wei
Keyword(s):  
Heisenberg Group ◽  
Weak Type ◽  
Acta Math ◽  
Hardy Operator ◽  
Sharp Constant ◽  
Hausdorff Operator ◽  
Weak Estimate ◽  
Hausdorff Operators

Abstract This paper is devoted to the weak and strong estimates for the linear and multilinear fractional Hausdorff operators on the Heisenberg group H n {{\mathbb{H}}}^{n} . A sharp strong estimate for T Φ m {T}_{\Phi }^{m} is obtained. As an application, we derive the sharp constant for the product Hardy operator on H n {{\mathbb{H}}}^{n} . Some weak-type ( p , q ) \left(p,q) ( 1 ≤ p ≤ ∞ ) \left(1\le p\le \infty ) estimates for T Φ , β {T}_{\Phi ,\beta } are also obtained. As applications, we calculate some sharp weak constants for the fractional Hausdorff operator on the Heisenberg group. Besides, we give an explicit weak estimate for T Φ , β → m {T}_{\Phi ,\overrightarrow{\beta }}^{m} under some mild assumptions on Φ \Phi . We extend the results of Guo et al. [Hausdorff operators on the Heisenberg group, Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 11, 1703–1714] to the fractional setting.

scholarly journals The Weighted Lp and BMO Estimates for Fractional Hausdorff Operators on the Heisenberg Group

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Guohua Zhang ◽  
Qianqian Li ◽  
Qingyan Wu
Keyword(s):  
Heisenberg Group ◽  
Hardy Spaces ◽  
Power Weights ◽  
Hausdorff Operators ◽  
Operator Norms

In the setting of Heisenberg group, we characterize those functions Φ, for which the fractional Hausdorff operators TΦ,β and Hausdorff operators TΦ, T˜Φ are bounded on Lp spaces with power weights, BMO space, and Hardy spaces, respectively. Meanwhile, the corresponding operator norms of TΦ and T˜Φ are worked out.

Hardy space estimates of Hausdorff operators on the Heisenberg group

2017 ◽  
Vol 164 ◽  
pp. 135-154 ◽  
Author(s):  
Qingyan Wu ◽  
Dashan Fan
Keyword(s):  
Hardy Space ◽  
Heisenberg Group ◽  
Hausdorff Operators

Weighted Herz space estimates for Hausdorff operators on the Heisenberg group

2017 ◽  
Vol 11 (3) ◽  
pp. 513-535 ◽  
Author(s):  
Jianmiao Ruan ◽  
Dashan Fan ◽  
Qingyan Wu
Keyword(s):  
Heisenberg Group ◽  
Herz Space ◽  
Hausdorff Operators
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