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.

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.

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 Hausdorff operators on holomorphic Hardy spaces and applications

2019 ◽  
Vol 150 (3) ◽  
pp. 1095-1112 ◽  
Author(s):  
Ha Duy Hung ◽  
Luong Dang Ky ◽  
Thai Thuan Quang
Keyword(s):  
Half Plane ◽  
Hardy Spaces ◽  
Hausdorff Operator ◽  
Upper Half Plane ◽  
Hausdorff Operators ◽  
Operator Norms ◽  
Image Position

AbstractThe aim of this paper is to characterize the non-negative functions φ defined on (0,∞) for which the Hausdorff operator $${\rm {\cal H}}_\varphi f(z) = \int_0^\infty f \left( {\displaystyle{z \over t}} \right)\displaystyle{{\varphi (t)} \over t}{\rm d}t$$is bounded on the Hardy spaces of the upper half-plane ${\rm {\cal H}}_a^p ({\open C}_ + )$, $p\in [1,\infty ]$. The corresponding operator norms and their applications are also given.

scholarly journals On the description of multidimensional normal Hausdorff operators on Lebesgue spaces

2020 ◽  
Vol 32 (1) ◽  
pp. 111-119 ◽  
Author(s):  
Adolf R. Mirotin
Keyword(s):  
Present Article ◽  
Spectral Representation ◽  
Research Field ◽  
Hausdorff Operator ◽  
Lebesgue Spaces ◽  
Summation Methods ◽  
Hausdorff Operators ◽  
Active Research ◽  
Matrix Symbol

AbstractHausdorff operators originated from some classical summation methods. Now this is an active research field. In the present article, a spectral representation for multidimensional normal Hausdorff operator is given. We show that normal Hausdorff operator in {L^{2}(\mathbb{R}^{n})} is unitary equivalent to the operator of multiplication by some matrix-valued function (its matrix symbol) in the space {L^{2}(\mathbb{R}^{n};\mathbb{C}^{2^{n}})}. Several corollaries that show that properties of a Hausdorff operator are closely related to the properties of its symbol are considered. In particular, the norm and the spectrum of such operators are described in terms of the symbol.

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 ◽  
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

scholarly journals Two-weighted estimates for multilinear Hausdorff operators on the Morrey–Herz spaces

2020 ◽  
Vol 5 (4) ◽  
pp. 1780-1813
Author(s):  
Nguyen Minh Chuong ◽  
Dao Van Duong ◽  
Nguyen Duc Duyet
Keyword(s):  
Herz Spaces ◽  
Weighted Estimates ◽  
Hausdorff Operators

scholarly journals Boundedness of Multidimensional Dunkl-Hausdorff Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Radouan Daher ◽  
Faouaz Saadi
Keyword(s):  
Hardy Space ◽  
Sufficient Conditions ◽  
Hausdorff Operator ◽  
Lebesgue Spaces ◽  
Dunkl Operators ◽  
Weighted Lebesgue Spaces ◽  
Hausdorff Operators

In the present paper, we introduce the multidimensional Dunkl-Hausdorff operator ℋκ and we give simple sufficient conditions so that these operators be bounded on the weighted lebesgue spaces Lκpℝn and in the Hardy space Hκ1ℝn associated with the Dunkl operators. We also determine the Dunkl-Hausdorff operator ℋκ∗ that is adjoint to ℋκ.

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