scholarly journals Operators with Gaussian kernel bounds on mixed Morrey spaces

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5219-5230 ◽  
Author(s):  
Francesca Anceschi ◽  
Christopher Goodrich ◽  
Andrea Scapellato
Keyword(s):  
Analytic Semigroup ◽  
Morrey Spaces ◽  
Gaussian Kernel ◽  
Fractional Operator ◽  
Lipschitz Spaces ◽  
Kernel Bounds

Let L be an analytic semigroup on L2(Rn) with Gaussian kernel bound, and let L-?/2 be the fractional operator associated to L for 0 < ? < n. In this paper, we prove some boundedness properties for the commutator [b,L-?/2] on Mixed Morrey spaces Lq,? (0,T,Lp,?(Rn)), when b belongs to BMO(Rn) or to suitable homogeneous Lipschitz spaces.

scholarly journals Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiheng Wang ◽  
Zengyan Si
Keyword(s):  
Analytic Semigroup ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Locally Integrable Function ◽  
Kernel Bounds ◽  
Necessary And Sufficient

LetLbe the infinitesimal generator of an analytic semigroup onL2(Rn)with Gaussian kernel bounds, and letL-α/2be the fractional integrals ofLfor0<α<n. For any locally integrable functionb, the commutators associated withL-α/2are defined by[b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). Whenb∈BMO(ω)(weightedBMOspace) orb∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of[b,L-α/2]on weighted Morrey spaces, respectively.

scholarly journals Applications of Littlewood-Paley Theory forB˙σ-Morrey Spaces to the Boundedness of Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Yasuo Komori-Furuya ◽  
Katsuo Matsuoka ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano
Keyword(s):  
Riesz Potential ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Lipschitz Spaces ◽  
Potential Operators

The boundedness of the various operators onB˙σ-Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization ofB˙σ-Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization ofB˙σ-Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators onB˙σ-Lipschitz spaces is discussed.

A note on vanishing Morrey → VMO result for fractional integrals of variable order

2020 ◽  
Vol 23 (1) ◽  
pp. 298-302 ◽  
Author(s):  
Humberto Rafeiro ◽  
Stefan Samko
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Variable Order ◽  
Fractional Operator ◽  
Limiting Case

AbstractIn the limiting case of Sobolev-Adams theorem for Morrey spaces of variable order we prove that the fractional operator of variable order maps the corresponding vanishing Morrey space into VMO.

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.

scholarly journals Estimates for Fractional Integral Operators and Linear Commutators on Certain Weighted Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-25 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Strong Type ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Kernel Bounds ◽  
Amalgam Spaces

In this paper, we first introduce some new classes of weighted amalgam spaces. Then, we give the weighted strong-type and weak-type estimates for fractional integral operators Iγ on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators b,Iγ generated by b and Iγ are established as well. In addition, we are going to study related problems about two-weight, weak-type inequalities for Iγ and b,Iγ on the weighted amalgam spaces and give some results. Based on these results and pointwise domination, we can prove norm inequalities involving fractional maximal operator Mγ and generalized fractional integrals ℒ−γ/2 in the context of weighted amalgam spaces, where 0<γ<n and L is the infinitesimal generator of an analytic semigroup on L2Rn with Gaussian kernel bounds.

scholarly journals Existence and Boundedness of Parametrized Marcinkiewicz Integral with Rough Kernel on Campanato Spaces

2006 ◽  
Vol 181 ◽  
pp. 103-148 ◽  
Author(s):  
Yong Ding ◽  
Qingying Xue ◽  
Kôzô Yabuta
Keyword(s):  
Single Point ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Marcinkiewicz Integral ◽  
Type Condition ◽  
Lipschitz Spaces ◽  
Area Function ◽  
Bmo Function ◽  
Lusin Area Function ◽  
Lipschitz Kernel

AbstractLet g(f), S(f), g*λ(f) be the Littlewood-Paley g function, Lusin area function, and Littlewood-Paley g*λ(f) function of f, respectively. In 1990 Chen Jiecheng and Wang Silei showed that if, for a BMO function f, one of the above functions is finite for a single point in ℝn, then it is finite a.e. on ℝn, and BMO boundedness holds. Recently, Sun Yongzhong extended this result to the case of Campanato spaces (i.e. Morrey spaces, BMO, and Lipschitz spaces). One of us improved his g*λ(f) result further, and treated parametrized Marcinkiewicz functions with Lipschitz kernel μρ(f), μρs(f) and μλ*,ρ(f). In this paper, we show that the same results hold also in the case of rough kernel satisfying Lp-Dini type condition.

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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