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.

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 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.

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 New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

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.

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