scholarly journals Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Wang ◽  
Wentan Yi
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Multiple Weights ◽  
Multilinear Fractional Integrals

We will study the boundedness properties of multilinear Calderón-Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

scholarly journals On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Sha He ◽  
Xiangxing Tao
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Rough Kernels ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Maximal Singular Integral

We study some multilinear operators with rough kernels. For the multilinear fractional integral operatorsTΩ,αAand the multilinear fractional maximal integral operatorsMΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weightsLp,κ(u,v)whenDγA∈Λ˙β  (|γ|=m-1)orDγA∈BMO  (|γ|=m-1). For the multilinear singular integral operatorsTΩAand the multilinear maximal singular integral operatorsMΩA, we show they are bounded on weighted Morrey spaces with two weightsLp,κ(u,v)ifDγA∈Λ˙β  (|γ|=m-1)and bounded on weighted Morrey spaces with one weightLp,κ(w)ifDγA∈BMO  (|γ|=m-1)form=1,2.

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 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.

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