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 Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

scholarly journals New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

2021 ◽  
Vol 6 (10) ◽  
pp. 11167-11186
Author(s):  
Hari M. Srivastava ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
General Family ◽  
Chebyshev Functional ◽  
Bounded Below

<abstract><p>The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.</p></abstract>

scholarly journals Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Canqin Tang ◽  
Qing Wu ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Type Inequality ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

scholarly journals Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hendra Gunawan ◽  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano ◽  
Idha Sihwaningrum
Keyword(s):  
Maximal Operator ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Littlewood Maximal Operator ◽  
Generalized Fractional Integral Operators

We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

scholarly journals Two-Weight, Weak-Type Norm Inequalities for Fractional Integral Operators and Commutators on Weighted Morrey and Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-23
Author(s):  
Hua Wang
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Weak Type ◽  
Extreme Case ◽  
Fractional Integral Operator ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Norm Estimates ◽  
Symbol Function ◽  
Amalgam Spaces

Let 0<γ<n and Iγ be the fractional integral operator of order γ, Iγfx=∫ℝnx−yγ−nfydy and let b,Iγ be the linear commutator generated by a symbol function b and Iγ, b,Iγfx=bx⋅Iγfx−Iγbfx. This paper is concerned with two-weight, weak-type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain Ap-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator Iγ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.

Fractional powers of operators and Riesz fractional integrals

1989 ◽  
Vol 112 (3-4) ◽  
pp. 237-247 ◽  
Author(s):  
S. E. Schiavone
Keyword(s):  
Banach Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fréchet Spaces ◽  
Test Functions ◽  
Fractional Powers ◽  
Fractional Integral Operators ◽  
Fractional Powers Of Operators

SynopsisIn this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.

scholarly journals Certain inequalities via generalized proportional Hadamard fractional integral operators

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Gauhar Rahman ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Aftab Khan ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
The Given ◽  
Hadamard Fractional Integrals ◽  
Hadamard Fractional Integral

Abstract In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results.

scholarly journals Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 896 ◽  
Author(s):  
Aditya Mani Mishra ◽  
Dumitru Baleanu ◽  
Fairouz Tchier ◽  
Sunil Dutt Purohit
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Integral Parameter ◽  
Fractional Operator ◽  
Weighted Function ◽  
Fractional Integral Operators ◽  
Chebyshev Function

An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.

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