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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Miroslav Pavlović (1996)
Publications de l'Institut Mathématique
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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.
Gurka, Petr, Opic, Bohumír (2008)
Banach Journal of Mathematical Analysis [electronic only]
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G. Okikiolu (1968)
Studia Mathematica
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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)].
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.
Soubhia, Ana, Camargo, Rubens, Oliveira, Edmundo, Vaz, Jayme (2010)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification 2010: 26A33, 33E12. The new result presented here is a theorem involving series in the three-parameter Mittag-Leffler function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional differential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Leffler function.
Yanping Chen, Xinfeng Wu, Honghai Liu (2014)
Studia Mathematica
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Some conditions implying vector-valued inequalities for the commutator of a fractional integral and a fractional maximal operator are established. The results obtained are substantial improvements and extensions of some known results.
R. K. Raina, Mamta Bolia (1997)
Rendiconti del Seminario Matematico della Università di Padova
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Atanackovic, Teodor, Stankovic, Bogoljub (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations...
Jan-Olov Strömberg, Richard Wheeden (1986)
Studia Mathematica
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S. Ombrosi, L. de Rosa (2003)
Publicacions Matemàtiques
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