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Search Results (4)

Search Parameters:
Keywords = weighted Zygmund space

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21 pages, 293 KiB  
Article
Composition Operators on Weighted Zygmund Spaces of the First Loo-keng Hua Domain
by Hong-Bin Bai
Symmetry 2024, 16(7), 828; https://doi.org/10.3390/sym16070828 - 1 Jul 2024
Viewed by 1161
Abstract
Let HEI denote the first Loo-keng Hua domain. In this paper, we obtain many elementary results on HEI by the continuous and careful discussions. In some applications, we obtain some necessary conditions or sufficient conditions for the boundedness and compactness of [...] Read more.
Let HEI denote the first Loo-keng Hua domain. In this paper, we obtain many elementary results on HEI by the continuous and careful discussions. In some applications, we obtain some necessary conditions or sufficient conditions for the boundedness and compactness of the composition operators on weighted Zygmund space defined on HEI. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
21 pages, 316 KiB  
Article
Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain
by Zhi-Jie Jiang
Axioms 2023, 12(12), 1131; https://doi.org/10.3390/axioms12121131 - 17 Dec 2023
Cited by 1 | Viewed by 1448
Abstract
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that [...] Read more.
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
13 pages, 323 KiB  
Article
Ap Weights in Directionally (γ,m) Limited Space and Applications
by Yu Yan, Yiming Wang and Yiming Lei
Mathematics 2022, 10(19), 3454; https://doi.org/10.3390/math10193454 - 22 Sep 2022
Viewed by 1499
Abstract
Let (X,d) be a directionally (γ,m)-limited space with every γ∈(0,∞). In this setting, we aim to study an analogue of the classical theory of [...] Read more.
Let (X,d) be a directionally (γ,m)-limited space with every γ∈(0,∞). In this setting, we aim to study an analogue of the classical theory of Ap(μ) weights. As an application, we establish some weighted estimates for the Hardy–Littlewood maximal operator. Then, we introduce the relationship between directionally (γ,m)-limited spaceand geometric doubling. Finally, we obtain the weighted norm inequalities of the Calderón–Zygmund operator and commutator in non-homogeneous space. Full article
19 pages, 357 KiB  
Article
Variation Inequalities for One-Sided Singular Integrals and Related Commutators
by Feng Liu, Seongtae Jhang, Sung-Kwun Oh and Zunwei Fu
Mathematics 2019, 7(10), 876; https://doi.org/10.3390/math7100876 - 20 Sep 2019
Cited by 3 | Viewed by 2462
Abstract
We establish one-sided weighted endpoint estimates for the ϱ -variation ( ϱ > 2 ) operators of one-sided singular integrals under certain priori assumption by applying one-sided Calderón–Zygmund argument. Using one-sided sharp maximal estimates, we further prove that the ϱ -variation operators of [...] Read more.
We establish one-sided weighted endpoint estimates for the ϱ -variation ( ϱ > 2 ) operators of one-sided singular integrals under certain priori assumption by applying one-sided Calderón–Zygmund argument. Using one-sided sharp maximal estimates, we further prove that the ϱ -variation operators of related commutators are bounded on one-sided weighted Lebesgue and Morrey spaces. In addition, we also show that these operators are bounded from one-sided weighted Morrey spaces to one-sided weighted Campanato spaces. As applications, we obtain some results for the λ -jump operators and the numbers of up-crossings. Our main results represent one-sided extensions of many previously known ones. Full article
(This article belongs to the Special Issue Inequalities)
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