scholarly journals Two-weight norm inequalities for the rough fractional integrals

2001 ◽  
Vol 25 (8) ◽  
pp. 517-524 ◽  
Author(s):  
Yong Ding ◽  
Chin-Cheng Lin
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Integrals ◽  
Weight Functions ◽  
Norm Inequalities ◽  
Fractional Maximal Operator

The authors give the weighted(Lp,Lq)-boundedness of the rough fractional integral operatorTΩ,αand the fractional maximal operatorMΩ,αwith two different weight functions.

scholarly journals MORREY SPACES AND FRACTIONAL OPERATORS

2010 ◽  
Vol 88 (2) ◽  
pp. 247-259 ◽  
Author(s):  
HITOSHI TANAKA
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Fractional Maximal Operator

AbstractThe relation between the fractional integral operator and the fractional maximal operator is investigated in the framework of Morrey spaces. Applications to the Fefferman–Phong and the Olsen inequalities are also included.

On the range and inversion of fractional integrals in weighted spaces

1982 ◽  
Vol 92 (1-2) ◽  
pp. 51-64 ◽  
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Integral Operator ◽  
Lebesgue Space ◽  
Inversion Formula ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Weighted Spaces ◽  
Fractional Integrals ◽  
Weight Functions ◽  
And Inversion ◽  
Unweighted Case

SynopsisThe weight functions w(x) for which the Riemann fractional integral operator Iα is bounded from the Lebesgue space Lp(wp) into Lq(wq), l/q = l/p −, have been characterized by Muckenhoupt and Wheeden. In this paper, we prove an inversion formula for Iα in the context of these weighted spaces and we also characterize the range of Iα as a subset of Lq(wq) Similar results are proved for other fractional integrals. These results may be viewed as weighted analogues of certain results of Stein and Zygmund, Herson and Heywood, Heywood, and Kober who considered the unweighted case, w(x) = l.

scholarly journals Morrey Spaces for Nonhomogeneous Metric Measure Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cao Yonghui ◽  
Zhou Jiang
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Marcinkiewicz Integral ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Definition Of

The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral operators.

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.

scholarly journals A basic study of a fractional integral operator with extended Mittag-Leffler kernel

2021 ◽  
Vol 6 (11) ◽  
pp. 12757-12770
Author(s):  
Gauhar Rahman ◽  
◽  
Iyad Suwan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Integrals ◽  
Basic Study ◽  
Basic Properties

<abstract><p>In this present paper, the basic properties of an extended Mittag-Leffler function are studied. We present some fractional integral and differential formulas of an extended Mittag-Leffler function. In addition, we introduce a new extension of Prabhakar type fractional integrals with an extended Mittag-Leffler function in the kernel. Also, we present certain basic properties of the generalized Prabhakar type fractional integrals.</p></abstract>

scholarly journals A WEAK-(p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES OVER METRIC MEASURE SPACES

2016 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Idha Sihwaningrum
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Metric Measure Spaces ◽  
Measure Spaces

This paper presents a weak-(p, q) inequality for fractional integral operator on Morrey spaces over metric measure spaces of nonhomogeneous type. Both parameters p and q are greater than or equal to one. The weak-(p, q) inequality is proved by employing an inequality involving maximal operator on the spaces under consideration.

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