Hausdorff Operators on Real Hardy Spaces H1 Over Homogeneous Spaces with Local Doubling Property

2021 ◽  
Vol 47 (2) ◽  
pp. 385-403
Author(s):  
A. R. Mirotin
Keyword(s):  
Hardy Spaces ◽  
Homogeneous Spaces ◽  
Doubling Property ◽  
Hausdorff Operators

scholarly journals Hausdorff operators on homogeneous spaces of locally compact groups

2020 ◽  
pp. 28-35
Author(s):  
Adolf R. Mirotin
Keyword(s):  
Hardy Spaces ◽  
Homogeneous Spaces ◽  
Research Area ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Hausdorff Operators ◽  
Active Research ◽  
Atomic Hardy Space ◽  
Active Research Area

Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.

scholarly journals Hardy spaces in Reinhardt domains, and Hausdorff operators

2009 ◽  
Vol 53 (4) ◽  
pp. 1033-1049 ◽  
Author(s):  
L. Aizenberg ◽  
E. Liflyand
Keyword(s):  
Hardy Spaces ◽  
Reinhardt Domains ◽  
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.

The fractional Hausdorff operators on the Hardy spaces H p (ℝ n )

2016 ◽  
Vol 42 (1) ◽  
pp. 1-17 ◽  
Author(s):  
J. Chen ◽  
D. Fan ◽  
X. Lin ◽  
J. Ruan
Keyword(s):  
Hardy Spaces ◽  
Hausdorff Operators

scholarly journals Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces

2019 ◽  
Vol 106 (1-2) ◽  
pp. 20-37 ◽  
Author(s):  
N. M. Chuong ◽  
D. V. Duong ◽  
K. H. Dung
Keyword(s):  
Hardy Spaces ◽  
Weighted Inequalities ◽  
Hausdorff Operators

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.

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