scholarly journals Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function inLp(·)Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Muhammad Sarwar ◽  
Ghulam Murtaza ◽  
Irshaad Ahmed
Keyword(s):  
Integral Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Sufficient Conditions ◽  
Fractional Integral Operator ◽  
Lebesgue Spaces ◽  
Higher Dimensional ◽  
Necessary And Sufficient ◽  
Decreasing Functions ◽  
Hardy Operators

One-weight inequalities with general weights for Riemann-Liouville transform andn-dimensional fractional integral operator in variable exponent Lebesgue spaces defined onRnare investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions inLp(x)spaces.

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Humberto Rafeiro ◽  
Makhmadiyor Yakhshiboev
Keyword(s):  
Integral Operator ◽  
Fractional Derivative ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Inverse Operator ◽  
Fractional Integral Operator ◽  
Left Inverse ◽  
Fractional Differentiation ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

AbstractAfter recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

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.

scholarly journals Fractional Operators in p -adic Variable Exponent Lebesgue Spaces and Application to p -adic Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Leonardo Fabio Chacón-Cortés ◽  
Humberto Rafeiro
Keyword(s):  
Cauchy Problem ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Uniqueness Of The Solution

In this paper, we prove the boundedness of the fractional maximal and the fractional integral operator in the p -adic variable exponent Lebesgue spaces. As an application, we show the existence and uniqueness of the solution for a nonhomogeneous Cauchy problem in the p -adic 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.

scholarly journals The boundedness of multilinear commutators on locally compact Vilenkin groups

2006 ◽  
Vol 4 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Canqin Tang
Keyword(s):  
Integral Operator ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Vilenkin Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Multilinear Commutators

LetGbe a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of multilinear commutators of fractional integral operator on Lebesgue spaces onG. Furthermore, the boundedness on Hardy spaces are also obtained in this paper.

scholarly journals Higher Order Commutators of Fractional Integral Operator on the Homogeneous Herz Spaces with Variable Exponent

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Liwei Wang ◽  
Meng Qu ◽  
Lisheng Shu
Keyword(s):  
Integral Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Higher Order ◽  
Lipschitz Functions ◽  
Fractional Integral Operator ◽  
Herz Spaces ◽  
Bmo Functions

By decomposing functions, we establish estimates for higher order commutators generated by fractional integral with BMO functions or the Lipschitz functions on the homogeneous Herz spaces with variable exponent. These estimates extend some known results in the literatures.

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.

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

Sign in / Sign up

Export Citation Format

Share Document