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Singular Integrals and Fractional Powers of Operators [PDF]

Transactions of the American Mathematical Society, 1971
Recently R. Wheeden studied a class of singular integral operators, the hypersingular integrals, as operators from L p α ( H ) L_p^\alpha (H) to L p ( H ) ; L p
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Morrey spaces and fractional integral operators

Expositiones Mathematicae, 2009
The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are established.
Eridani, Vakhtang Kokilashvili, Alexander Meskhi   +2 more
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A Note on Generalized Fractional Integral Operators on Generalized Morrey Spaces

Boundary Value Problems, 2009
We show some inequalities for generalized fractional integral operators on generalized Morrey spaces. We also show the boundedness property of the generalized fractional integral operators on the predual of the generalized Morrey spaces.
Yoshihiro Sawano, Satoko Sugano, Hitoshi Tanaka   +2 more
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Bounds of a Unified Integral Operator via Exponentially s,m-Convexity and Their Consequences

Journal of Function Spaces, 2020
Various known fractional and conformable integral operators can be obtained from a unified integral operator. The aim of this paper is to find bounds of this unified integral operator via exponentially s,m-convex functions.
Yi Hu, Ghulam Farid, Zijiang, Kahkashan Mahreen   +3 more
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Novel Approaches for Differentiable Convex Functions via the Proportional Caputo-Hybrid Operators

Fractal and Fractional, 2022
This study is built on the relationship between inequality theory and fractional analysis. Thanks to the new fractional operators and based on the proportional Caputo-hybrid operators, integral inequalities containing new approaches are obtained for ...
Mustafa Gürbüz, Ahmet Ocak Akdemir, Mustafa Ali Dokuyucu   +2 more
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Fractional Integral Operators

, 2023
equipped with a positive Radon measure .
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Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions

Journal of Mathematics, 2020
In this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions.
Chahn Yong Jung, Muhammad Yussouf, Yu-Ming Chu, Ghulam Farid, Shin Min Kang   +4 more
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On local fractional integral inequalities via generalized (h˜1,h˜2)\left({\tilde{h}}_{1},{\tilde{h}}_{2})-preinvexity involving local fractional integral operators with Mittag-Leffler kernel

Demonstratio Mathematica, 2023
Local fractional integral inequalities of Hermite-Hadamard type involving local fractional integral operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities.
Vivas-Cortez Miguel, Bibi Maria, Muddassar Muhammad, Al-Sa’di Sa’ud   +3 more
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Fractional transformations of generalised functions [PDF]

, 2009
A distributional theory of fractional transformations is developed. A constructive approach, based on the eigenfunction expansion method pioneered by A. H.
Khan, Khaula Naeem, Lamb, Wilson, McBride, Adam C.   +2 more
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Applications of the Atangana–Baleanu Fractional Integral Operator

Symmetry, 2022
Applications of the Atangana–Baleanu fractional integral were considered in recent studies related to geometric function theory to obtain interesting differential subordinations. Additionally, the multiplier transformation was used in many studies, providing elegant results.
Alina Alb Lupas, Adriana Catas
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