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 FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous 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 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.

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 A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces

2021 ◽  
Vol 5 (1) ◽  
pp. 7
Author(s):  
Lütfi Akın
Keyword(s):  
Integral Operator ◽  
Harmonic Analysis ◽  
Time Scales ◽  
Variable Exponent ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Important Place ◽  
New Approach ◽  
Variable Exponent Lebesgue Spaces ◽  
Important Study

Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond integral operator to the norm of the centered fractional maximal diamond integral operator on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales.

Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces

2020 ◽  
Vol 70 (4) ◽  
pp. 893-902
Author(s):  
Ismail Ekincioglu ◽  
Vagif S. Guliyev ◽  
Esra Kaya
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Bessel Differential Operator

AbstractIn this paper, we prove the boundedness of the Bn maximal operator and Bn singular integral operators associated with the Laplace-Bessel differential operator ΔBn on variable exponent Lebesgue spaces.

Chebyshev type inequality containing a fractional integral operator with a multi-index Mittag-Leffler function as a kernel

Analysis ◽  
2021 ◽  
Vol 41 (1) ◽  
pp. 61-67
Author(s):  
Kamlesh Jangid ◽  
S. D. Purohit ◽  
Kottakkaran Sooppy Nisar ◽  
Serkan Araci
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Multi Index ◽  
Type Integral ◽  
Special Case

Abstract In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral operators present in the literature.

scholarly journals Multilinear strongly singular integral operators with generalized kernels and applications

2021 ◽  
Vol 6 (12) ◽  
pp. 13533-13551
Author(s):  
Shuhui Yang ◽  
◽  
Yan Lin
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces

<abstract><p>In this paper, the authors study the boundedness properties of a class of multilinear strongly singular integral operator with generalized kernels on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces, respectively. Moreover, the types $ L^{\infty}\times \dots \times L^{\infty}\rightarrow BMO $ and $ BMO\times \dots \times BMO\rightarrow BMO $ endpoint estimates are also obtained.</p></abstract>

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