A Proof of the Hardy-Littlewood Theorem on Fractional Integration and a Generalization
Miroslav Pavlović (1996)
Publications de l'Institut Mathématique
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Displaying similar documents to “Hardy inequality of fractional order.”
A Proof of the Hardy-Littlewood Theorem on Fractional Integration and a Generalization
Fractional Hardy inequality with a remainder term
Bartłomiej Dyda (2011)
Colloquium Mathematicae
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We prove a Hardy inequality for the fractional Laplacian on the interval with the optimal constant and additional lower order term. As a consequence, we also obtain a fractional Hardy inequality with the best constant and an extra lower order term for general domains, following the method of M. Loss and C. Sloane [J. Funct. Anal. 259 (2010)].
Fractional Hardy inequalities and visibility of the boundary
Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas (2014)
Studia Mathematica
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We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.
Fractional Hardy-Sobolev-Maz'ya inequality for domains
Bartłomiej Dyda, Rupert L. Frank (2012)
Studia Mathematica
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We prove a fractional version of the Hardy-Sobolev-Maz’ya inequality for arbitrary domains and norms with p ≥ 2. This inequality combines the fractional Sobolev and the fractional Hardy inequality into a single inequality, while keeping the sharp constant in the Hardy inequality.
Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents
Hongbin Wang, Chenchen Niu (2024)
Czechoslovak Mathematical Journal
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We introduce a type of -dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.
Some properties of fractional integrals. II.
G. H., and J.E.Littlewood, Hardy (1932)
Mathematische Zeitschrift
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Some properties of fractional integrals. I.
G. H., und J. Hardy, J. E. Littlewood (1928)
Mathematische Zeitschrift
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Note on the fractional parts of λθⁿ
Masayoshi Hata (2005)
Acta Arithmetica
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On a sum of fractional parts
B. Martić (1964)
Matematički Vesnik
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Existence of solutions of generalized fractional differential equation with nonlocal initial condition
Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)
Mathematica Bohemica
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This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.
On fractional derivatives
Helena Musielak (1973)
Colloquium Mathematicae
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Extensions of Hardy-Littlewood inequalities.
Lou, Zengjian (1994)
International Journal of Mathematics and Mathematical Sciences
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A Note On Fractional Integration
Branislav Martić (1973)
Publications de l'Institut Mathématique
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Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis
Astha Chauhan, Rajan Arora (2019)
Communications in Mathematics
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In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation...