scholarly journals Fractional integral operators on Herz spaces for supercritical indices

2011 ◽  
Vol 9 (2) ◽  
pp. 179-190 ◽  
Author(s):  
Yasuo Komori-Furuya
Keyword(s):  
Function Space ◽  
Fractional Integral ◽  
Integral Operators ◽  
Lipschitz Space ◽  
Herz Spaces ◽  
Fractional Integral Operators

We consider the boundedness of fractional integral operatorsIβon Herz spacesKqα,p(Rn), whereq≥n/β. We introduce a new function space that is a variant of Lipschitz space. Our results are optimal.

scholarly journals Boundedness of several operators on weighted Herz spaces

2009 ◽  
Vol 7 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Yasuo Komori ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Fractional Integral Operators

We consider the boundedness of singular integral operators and fractional integral operators on weighted Herz spaces. For this purpose we introduce generalized Herz space. Our results are the best possible.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

scholarly journals Two-weight norm inequalities for fractional integral operators with $A_{\lambda,\infty}$ weights

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Junren Pan ◽  
Wenchang Sun
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Type Estimate ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
New Class ◽  
Formula Type

Abstract In this paper, we introduce a new class of weights, the $A_{\lambda, \infty}$Aλ,∞ weights, which contains the classical $A_{\infty}$A∞ weights. We prove a mixed $A_{p,q}$Ap,q–$A_{\lambda,\infty}$Aλ,∞ type estimate for fractional integral operators.

On Chebychev type inequalities for fractional integral operators

2017 ◽  
Author(s):  
Fuat Usta ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators
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