scholarly journals Boundedness for Commutators of Rough p -Adic Hardy Operator on p -Adic Central Morrey Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Naqash Sarfraz ◽  
Muhammad Aslam ◽  
Fahd Jarad
Keyword(s):  
Present Article ◽  
Morrey Spaces ◽  
Hardy Operator ◽  
Lebesgue Spaces

In the present article we obtain the boundedness for commutators of rough p -adic Hardy operator on p -adic central Morrey spaces. Furthermore, we also acquire the boundedness of rough p -adic Hardy operator on Lebesgue spaces.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Commutators of the Bilinear Hardy Operator on Herz Type Spaces with Variable Exponents

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shengrong Wang ◽  
Jingshi Xu
Keyword(s):  
Morrey Spaces ◽  
Hardy Operator ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Bmo Functions ◽  
Type Spaces

In this paper, we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of Herz spaces and Herz-Morrey spaces with variable exponents.

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.

Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces

2020 ◽  
Vol 27 (3) ◽  
pp. 433-439
Author(s):  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Doubling Measure ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces

AbstractThe predual spaces of generalized grand Morrey spaces over non-doubling measure spaces are investigated. The case of the grand Lebesgue spaces is covered, which is also new. An example shows that the modification of Morrey spaces is essential.

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 Littlewood-Paley spaces

2011 ◽  
Vol 108 (1) ◽  
pp. 77 ◽  
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Hardy Spaces ◽  
Orlicz Spaces ◽  
Morrey Spaces ◽  
Function Spaces ◽  
Unified Framework ◽  
Lebesgue Spaces ◽  
Banach Function Spaces

We introduce the Littlewood-Paley spaces in which the Lebesgue spaces, the Hardy spaces, the Orlicz spaces, the Lorentz-Karamata spaces, the r.-i. quasi-Banach function spaces and the Morrey spaces reside. The Littlewood-Paley spaces provide a unified framework for the study of some important function spaces arising in analysis.

scholarly journals Weighted Estimates for Commutator of Rough p -Adic Fractional Hardy Operator on Weighted p -Adic Herz–Morrey Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Naqash Sarfraz ◽  
Doaa Filali ◽  
Amjad Hussain ◽  
Fahd Jarad
Keyword(s):  
Morrey Spaces ◽  
Hardy Operator ◽  
Lipschitz Spaces ◽  
Weighted Estimates ◽  
Type Spaces ◽  
Current Article ◽  
Symbol Function

The current article investigates the boundedness criteria for the commutator of rough p -adic fractional Hardy operator on weighted p -adic Lebesgue and Herz-type spaces with the symbol function from weighted p -adic bounded mean oscillations and weighted p -adic Lipschitz spaces.

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