Endpoint Estimates for Generalized Multilinear Fractional Integrals on the Non-homogeneous Metric Spaces

2018 ◽  
Vol 39 (4) ◽  
pp. 721-738
Author(s):  
Jiecheng Chen ◽  
Xiaoli Chen ◽  
Fangting Jin
Keyword(s):  
Metric Spaces ◽  
Fractional Integrals ◽  
Multilinear Fractional Integrals

scholarly journals Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Mieczysław Mastyło ◽  
Alexander Meskhi
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Potential Operator ◽  
Norm Estimates ◽  
Riesz Potential Operator ◽  
Weight Problems ◽  
Multilinear Fractional Integrals ◽  
Necessary And Sufficient

AbstractWe derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in particular, we derive necessary and sufficient conditions guaranteeing the trace type inequality for this operator. We also establish the Fefferman-Stein type inequality, and obtain one-weight criteria when a weight function is of product type. As a consequence, appropriate results for multilinear Riesz potential operator with product kernels follow.

scholarly journals On multilinear fractional integrals

1992 ◽  
Vol 102 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Loukas Grafakos
Keyword(s):  
Fractional Integrals ◽  
Multilinear Fractional Integrals

scholarly journals Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Wang ◽  
Wentan Yi
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Multiple Weights ◽  
Multilinear Fractional Integrals

We will study the boundedness properties of multilinear Calderón-Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

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 Contributions of the fixed point technique to solve the 2D Volterra integral equations, Riemann–Liouville fractional integrals, and Atangana–Baleanu integral operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hasanen A. Hammad ◽  
Hassen Aydi ◽  
Nabil Mlaiki
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Integral Operators ◽  
Volterra Integral Equations ◽  
Fractional Integrals ◽  
Uniqueness Of Solutions ◽  
Mild Conditions ◽  
Contractive Type ◽  
Theoretical Results

AbstractIn this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, $\eta _{\gimel }^{\nu }$ η ℷ ν -metric spaces) are obtained. Moreover, some related consequences dealing with a common fixed point concept and nontrivial examples to support our results are presented. Ultimately, we use the theoretical results to discuss the existence and uniqueness of solutions of 2D Volterra integral equations, Riemann–Liouville integrals and Atangana–Baleanu integral operators are given.

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