Weighted Inequalities for the Fractional Maximal Operator and the Fractional Integral Operator

1996 ◽  
Vol 15 (2) ◽  
pp. 309-328
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Weighted Inequalities ◽  
Fractional Maximal Operator

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.

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 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.

On the Boundedness of Classical Operators on Weighted Lorentz Spaces

1998 ◽  
Vol 5 (2) ◽  
pp. 177-200
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Integral Operator ◽  
Lorentz Space ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Zygmund Operator ◽  
Classical Operator ◽  
Weighted Lorentz Spaces ◽  
Weighted Lorentz Space

Abstract Conditions on weights 𝑢(·), υ(·) are given so that a classical operator T sends the weighted Lorentz space Lrs (υd𝑥) into Lpq (υd𝑥). Here T is either a fractional maximal operator Mα or a fractional integral operator Iα or a Calderón–Zygmund operator. A characterization of this boundedness is obtained for Mα and Iα when the weights have some usual properties and max(r, s) ≤ min(p, q).

scholarly journals A WEAK-(p, q) INEQUALITY FOR FRACTIONAL INTEGRAL OPERATOR ON MORREY SPACES VIA HEDBERG TYPE INEQUALITY

2016 ◽  
Vol 8 (2) ◽  
pp. 103
Author(s):  
Idha Sihwaningrum ◽  
Hendra Gunawan
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Morrey Spaces ◽  
Fractional Integral Operator

By employing the growth measure, in this paper we prove the weak-(p, q) inequality for fractional integral operator on Morrey spaces via Hedberg type inequality. The proof also needs the weak-(p, p) inequality of the maximal operator in the same spaces.

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