scholarly journals Weighted Multilinear Hardy Operators on Herz Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shuli Gong ◽  
Zunwei Fu ◽  
Bolin Ma
Keyword(s):  
Weight Function ◽  
Sufficient Condition ◽  
Herz Spaces ◽  
Type Spaces ◽  
Hardy Operators

This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product Morrey-Herz spaces.

Commutators of weighted Hardy operators on Herz-type spaces

2011 ◽  
Vol 101 (3) ◽  
pp. 267-273 ◽  
Author(s):  
Canqin Tang ◽  
Feien Xue ◽  
Yu Zhou
Keyword(s):  
Type Spaces ◽  
Weighted Hardy Operators ◽  
Hardy Operators

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 Boundedness of Weighted Hardy Operator and Its Adjoint on Triebel-Lizorkin-Type Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Canqin Tang ◽  
Ruohong Zhou
Keyword(s):  
Weight Function ◽  
Adjoint Operator ◽  
Hardy Operator ◽  
Necessary Condition ◽  
Hausdorff Spaces ◽  
Type Spaces ◽  
Sufficient And Necessary Condition

Letp∈[1,∞],q∈[1,∞),τ∈(0,∞), andα∈(0,1)such thatτ>1/p-1/qandα≤n(1/p-τ), letUψbe the weighted Hardy operator andVψits adjoint operator with respect to the weight functionψ. In this paper, the authors establish a sufficient and necessary condition on weight functionψto ensure the boundedness ofUψandVψon the Triebel-Lizorkin-type spacesḞp,qα,τ(ℝn)and their predual spaces, Triebel-Lizorkin-Hausdorff spaces, which unify and generalize the known results onQ-type spaces.

scholarly journals Average Operators on Rectangular Herz Spaces

2016 ◽  
Vol 65 (1) ◽  
pp. 61-70
Author(s):  
Carolina Espinoza-Villalva ◽  
Martha Guzmán-Partida
Keyword(s):  
Herz Spaces ◽  
Continuity Properties ◽  
Type Spaces

Abstract We introduce a family of Herz type spaces considering rectangles instead of balls and we study continuity properties of some average operators acting on them.

scholarly journals Endpoint Estimates for Fractional Hardy Operators and Their Commutators on Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jiang Zhou ◽  
Dinghuai Wang
Keyword(s):  
Hardy Spaces ◽  
Herz Spaces ◽  
Multilinear Commutators ◽  
Hardy Operators

(Hpℝn,Lqℝn)bounds of fractional Hardy operators are obtained. Moreover, the estimates for commutators of fractional Hardy operators on Hardy spaces are worked out. It is also proved that the commutators of fractional Hardy operators are mapped from the Herz-type Hardy spaces into the Herz spaces. The estimates for multilinear commutators of fractional Hardy operators are also discussed.

scholarly journals Estimates for Commutators of Bilinear Fractional p -Adic Hardy Operator on Herz-Type Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Amjad Hussain ◽  
Naqash Sarfraz ◽  
Ilyas Khan ◽  
Aisha M. Alqahtani
Keyword(s):  
Hardy Operator ◽  
Herz Spaces ◽  
Lipschitz Spaces ◽  
Type Spaces ◽  
Current Article ◽  
Symbol Function

In the current article, we investigate the boundedness of commutators of the bilinear fractional p -adic Hardy operator on p -adic Herz spaces and p -adic Morrey-Herz spaces by considering the symbol function from central bounded mean oscillations and Lipschitz spaces.

QpSpaces and Dirichlet Type Spaces

2017 ◽  
Vol 60 (4) ◽  
pp. 690-704 ◽  
Author(s):  
Guanlong Bao ◽  
Nihat Gökhan Gögüs ◽  
Stamatis Pouliasis
Keyword(s):  
Hilbert Spaces ◽  
Invariant Function ◽  
Open Unit ◽  
Sufficient Condition ◽  
Borel Measures ◽  
Dirichlet Type ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Decomposition Theorems ◽  
Dirichlet Type Space

AbstractIn this paper, we show that the Möbius invariant function space Qpcan be generated by variant Dirichlet type spaces 𝒟μ,pinduced by finite positive Borel measures μ on the open unit disk. A criterion for the equality between the space 𝒟μ,pand the usual Dirichlet type space 𝒟pis given. We obtain a sufficient condition to construct different 𝒟μ,pspaces and provide examples. We establish decomposition theorems for 𝒟μ,pspaces and prove that the non-Hilbert space Qpis equal to the intersection of Hilbert spaces 𝒟μ,p. As an application of the relation between Qpand 𝒟μ,pspaces, we also obtain that there exist different 𝒟μ,pspaces; this is a trick to prove the existence without constructing examples.

scholarly journals A note on the boundedness of sublinear operators on grand variable Herz spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hammad Nafis ◽  
Humberto Rafeiro ◽  
Muhammad Asad Zaighum
Keyword(s):  
Herz Spaces ◽  
Sublinear Operators ◽  
Type Spaces

AbstractIn this paper, we introduce grand variable Herz type spaces using discrete grand spaces and prove the boundedness of sublinear operators on these spaces.

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