scholarly journals A Hausdorff Operator with Commuting Family of Perturbation Matrices Is a Non-Riesz Operator

2020 ◽  
Vol 27 (4) ◽  
pp. 484-490
Author(s):  
A. R. Mirotin
Keyword(s):  
Hausdorff Operator ◽  
Riesz Operator

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.

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 A trace problem for associate Morrey potentials

2018 ◽  
Vol 7 (3) ◽  
pp. 407-424 ◽  
Author(s):  
Jie Xiao
Keyword(s):  
Radon Measure ◽  
Morrey Spaces ◽  
Riesz Operator

AbstractAs a solution to the restriction question for associate Morrey potentials (Question 1.1), this paper characterizes a Radon measure μ on {\mathbb{R}^{n}} such that the Riesz operator {I_{\alpha}} maps the associate Morrey spaces {H^{p,\kappa}_{1}\subset H^{p,\kappa}} to the μ-induced Morrey spaces {L^{q,\lambda}_{\mu}\subset L^{q,\lambda}_{\mu,\infty}} continuously. The discovered restriction/trace principle (Theorem 1.2) is brand-new, and its demonstration is non-trivial.

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.

Weighted Morrey–Herz space estimates for rough Hausdorff operator and its commutators

2019 ◽  
Vol 11 (2) ◽  
pp. 753-787 ◽  
Author(s):  
Nguyen Minh Chuong ◽  
Dao Van Duong ◽  
Nguyen Duc Duyet
Keyword(s):  
Herz Space ◽  
Hausdorff Operator
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