scholarly journals Boundedness ofp-Adic Hardy Operators and Their Commutators onp-Adic Central Morrey and BMO Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qing Yan Wu ◽  
Ling Mi ◽  
Zun Wei Fu
Keyword(s):  
Morrey Spaces ◽  
Sharp Bounds ◽  
Bmo Spaces ◽  
Hardy Operators

We obtain the sharp bounds ofp-adic Hardy operators onp-adic central Morrey spaces andp-adicλ-central BMO spaces, respectively. We also establish theλ-central BMO estimates for commutators ofp-adic Hardy operators onp-adic central Morrey spaces.

scholarly journals Weighted multilinear p-adic Hardy operators and commutators

2017 ◽  
Vol 15 (1) ◽  
pp. 1623-1634
Author(s):  
Ronghui Liu ◽  
Jiang Zhou
Keyword(s):  
Morrey Spaces ◽  
Special Structure ◽  
Euclidean Spaces ◽  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Hardy Operators

Abstract In this paper, the weighted multilinear p-adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p-adic Lebesgue spaces, and the product of p-adic central Morrey spaces, the product of p-adic Morrey spaces, respectively. Moreover, we establish the boundedness of commutators of the weighted multilinear p-adic Hardy operators on the product of p-adic central Morrey spaces. However, it’s worth mentioning that these results are different from that on Euclidean spaces due to the special structure of the p-adic fields.

scholarly journals Weighted multilinear Hardy operators and commutators

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Zun Wei Fu ◽  
Shu Li Gong ◽  
Shan Zhen Lu ◽  
Wen Yuan
Keyword(s):  
Necessary Conditions ◽  
Morrey Spaces ◽  
Bmo Space ◽  
Weight Functions ◽  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Sharp Estimates ◽  
Sufficient And Necessary Conditions ◽  
Hardy Operators

AbstractIn this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted multilinear Hardy operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Riemann–Liouville and Weyl.

scholarly journals A Weighted Variant of Riemann-Liouville Fractional Integrals onℝn

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Zun Wei Fu ◽  
Shan Zhen Lu ◽  
Wen Yuan
Keyword(s):  
Morrey Spaces ◽  
Fractional Integrals ◽  
Bmo Space ◽  
Necessary Condition ◽  
Weight Functions ◽  
Sharp Estimates ◽  
Bmo Spaces ◽  
Weighted Hardy Operators ◽  
Sufficient And Necessary Condition ◽  
Hardy Operators

We introduce certain type of weighted variant of Riemann-Liouville fractional integral onℝnand obtain its sharp bounds on the central Morrey andλ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols inλ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.

scholarly journals Weighted Hardy operators in local generalized Orlicz-Morrey spaces

2021 ◽  
Vol 13 (2) ◽  
pp. 522-533
Author(s):  
C. Aykol ◽  
Z.O. Azizova ◽  
J.J. Hasanov
Keyword(s):  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Strong Type ◽  
Young Functions ◽  
Weighted Hardy Operators ◽  
Hardy Operators

In this paper, we find sufficient conditions on general Young functions $(\Phi, \Psi)$ and the functions $(\varphi_1,\varphi_2)$ ensuring that the weighted Hardy operators $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ are of strong type from a local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ into another local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$. We also obtain the boundedness of the commutators of $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ from $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ to $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.

Sharp bounds for Hardy operators on product spaces

2018 ◽  
Vol 38 (2) ◽  
pp. 441-449
Author(s):  
Mingquan WEI ◽  
Dunyan YAN
Keyword(s):  
Product Spaces ◽  
Sharp Bounds ◽  
Hardy Operators

Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces

2021 ◽  
Vol 24 (6) ◽  
pp. 1643-1669
Author(s):  
Natasha Samko
Keyword(s):  
Upper Bound ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Target Space ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Measure Spaces ◽  
Hardy Operators ◽  
Hardy Type Operators

Abstract We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure spaces for a certain class of “radial” weights. Quasi-metric measure spaces may include, in particular, sets of fractional dimentsions. We prove theorems on the boundedness of commutators with CMO coefficients of these operators. Given a domain Morrey space 𝓛 p,φ (X) for the fractional Hardy operators or their commutators, we pay a special attention to the study of the range of the exponent q of the target space 𝓛 q,ψ (X). In particular, in the case of classical Morrey spaces, we provide the upper bound of this range which is greater than the known Adams exponent.

scholarly journals Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Bijun Ren ◽  
Enbin Zhang
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Linear Operators ◽  
Identity Operator ◽  
Zygmund Operator ◽  
Weighted Bmo ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Bmo Spaces ◽  
Toeplitz Type Operator

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

scholarly journals Sharp Bounds for Generalized m -Linear n -Dimensional p -Adic Hardy-Littlewood-Pólya Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiang Li ◽  
Xiran Zhang ◽  
Qianjun He
Keyword(s):  
Morrey Spaces ◽  
Power Weight ◽  
Sharp Bounds

In this paper, we study the sharp bounds for the generalized m -linear n -dimensional p -adic Hardy-Littlewood-Pólya operator on central and noncentral p -adic Morrey spaces with power weight. As an application, the sharp bounds for the p -adic Hardy-Littlewood-Pólya operator on corresponding Morrey spaces are obtained. These results generalize substantially some well-known results.

scholarly journals Estimates for the Commutators of p-Adic Hausdorff Operator on Herz-Morrey Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 127 ◽  
Author(s):  
Naqash Sarfraz ◽  
Amjad Hussain
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Hausdorff Operator ◽  
Lipschitz Spaces ◽  
Bmo Spaces

In this paper, we investigate the boundedness of commutators of matrix Hausdorff operator on the weighted p-adic Herz-Morrey space with the symbol functions in weighted central bounded mean oscillations (BMO) and Lipschitz spaces. In addition, a result showing boundedness of Hausdorff operator on weighted p-adic λ -central BMO spaces is provided as well.

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