Vector-valued inequalities for the commutators of fractional integrals with rough kernels

2014 ◽  
Vol 222 (2) ◽  
pp. 97-122 ◽  
Author(s):  
Yanping Chen ◽  
Xinfeng Wu ◽  
Honghai Liu
Keyword(s):  
Fractional Integrals ◽  
Rough Kernels ◽  
Vector Valued

scholarly journals Weighted Estimates for Rough Maximal Functions with Applications to Angular Integrability

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Feng Liu ◽  
Fangfang Xu
Keyword(s):  
Function Spaces ◽  
Maximal Functions ◽  
Rough Kernels ◽  
Weighted Estimates ◽  
Polynomial Curves ◽  
Definition Of ◽  
Vector Valued Function ◽  
Vector Valued

In this note we establish certain weighted estimates for a class of maximal functions with rough kernels along “polynomial curves” on Rn. As applications, we obtain the bounds of the above operators on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces, and on the vector-valued function spaces. Particularly, the above bounds are independent of the coefficients of the polynomials in the definition of the operators.

scholarly journals Rough Multilinear Fractional Integrals on Weighted Morrey Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiao Li ◽  
Runqing Cui
Keyword(s):  
Morrey Spaces ◽  
Higher Order ◽  
Fractional Integrals ◽  
Fractional Operators ◽  
Rough Kernels ◽  
Weighted Morrey Spaces ◽  
Multilinear Fractional Integrals ◽  
Multilinear Fractional Operators

It is showed that a class of multilinear fractional operators with rough kernels, which are similar to the higher-order commutators for the rough fractional integrals, are bounded on the weighted Morrey spaces.

scholarly journals Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Hongbin Wang ◽  
Jiajia Wang ◽  
Zunwei Fu
Keyword(s):  
Variable Exponent ◽  
Morrey Space ◽  
Homogeneous Function ◽  
Fractional Integrals ◽  
Herz Space ◽  
Degree Zero ◽  
Rough Kernels ◽  
Bmo Function ◽  
Central Morrey Space ◽  
Homogeneous Fractional Integral Operator

We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator TΩ,σ and its commutator [b,TΩ,σ] on Morrey-Herz space with variable exponent, where Ω∈Ls(Sn-1) for s≥1 is a homogeneous function of degree zero, 0<σ<n, and b is a BMO function.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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