scholarly journals The Boundedness of Multilinear Fractional Integral Operators with Variable Kernel on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 06 (01) ◽  
pp. 72-80
Author(s):  
秋阅 万
Keyword(s):  
Variable Exponent ◽  
Fractional Integral ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Multilinear Fractional Integral ◽  
Variable Exponent Lebesgue Spaces

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.

Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces

2014 ◽  
Vol 51 (3) ◽  
pp. 384-406 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Measure Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Integral Operators ◽  
Doubling Condition ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Norm Estimates ◽  
Variable Exponent Lebesgue Spaces ◽  
Necessary And Sufficient

Two-weight norm estimates for sublinear integral operators involving Hardy-Littlewood maximal, Calderón-Zygmund and fractional integral operators in variable exponent Lebesgue spaces are derived. Operators and the space are defined on a quasi-metric measure space with doubling condition. The derived conditions are written in terms ofLp(·)norms and are simultaneously necessary and sufficient for appropriate inequalities for maximal and fractional integral operators mainly in the case when weights are of radial type.

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 Multilinear fractional integral operators on central Morrey spaces with variable exponent

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongbin Wang ◽  
Jingshi Xu
Keyword(s):  
Variable Exponent ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operators ◽  
Multilinear Fractional Integral

AbstractIn this paper, we obtain the boundedness of the multilinear fractional integral operators and their commutators on central Morrey spaces with variable exponent.

A note on fractional integral operators defined by weights and non-doubling measures

2010 ◽  
Vol 106 (2) ◽  
pp. 283 ◽  
Author(s):  
Oscar Blasco ◽  
Vicente Casanova ◽  
Joaquín Motos
Keyword(s):  
Measure Space ◽  
Fractional Integral ◽  
Integral Operators ◽  
Metric Measure Space ◽  
Integral Type ◽  
Lebesgue Spaces ◽  
Lipschitz Spaces ◽  
Fractional Integral Operators ◽  
Doubling Measures

Given a metric measure space $(X,d,\mu)$, a weight $w$ defined on $(0,\infty)$ and a kernel $k_w(x,y)$ satisfying the standard fractional integral type estimates, we study the boundedness of the operators $K_w f(x)=\int_X k_w(x,y)f(y)\,d\mu(y)$ and $\tilde K_w f(x)=\int_X (k_w(x,y)-k_w(x_0,y))f(y)\,d\mu(y)$ on Lebesgue spaces $L^p(\mu)$ and generalized Lipschitz spaces $\mathrm{Lip}_\phi$, respectively, for certain range of the parameters depending on the $n$-dimension of $\mu$ and some indices associated to the weight $w$.

On the Boundedness of Multilinear Fractional Integral Operators

2019 ◽  
Vol 30 (1) ◽  
pp. 667-679
Author(s):  
Vakhtang Kokilashvili ◽  
Mieczysław Mastyło ◽  
Alexander Meskhi
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Multilinear Fractional Integral

Compactness criteria for fractional integral operators

2019 ◽  
Vol 22 (5) ◽  
pp. 1269-1283 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Mieczysław Mastyło ◽  
Alexander Meskhi
Keyword(s):  
Integral Operator ◽  
Measure Space ◽  
Fractional Integral ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Bounded Domains ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Rectifiable Curves ◽  
Necessary And Sufficient

Abstract We establish necessary and sufficient conditions for the compactness of fractional integral operators from Lp(X, μ) to Lq(X, μ) with 1 < p < q < ∞, where μ is a measure on a quasi-metric measure space X. As an application we obtain criteria for the compactness of fractional integral operators defined in weighted Lebesgue spaces over bounded domains of the Euclidean space ℝn with the Lebesgue measure, and also for the fractional integral operator associated to rectifiable curves of the complex plane.

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