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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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)].
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.
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.
G. H., and J.E.Littlewood, Hardy (1932)
Mathematische Zeitschrift
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G. H., und J. Hardy, J. E. Littlewood (1928)
Mathematische Zeitschrift
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Masayoshi Hata (2005)
Acta Arithmetica
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B. Martić (1964)
Matematički Vesnik
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Helena Musielak (1973)
Colloquium Mathematicae
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Lou, Zengjian (1994)
International Journal of Mathematics and Mathematical Sciences
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Branislav Martić (1973)
Publications de l'Institut Mathématique
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Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka (2011)
Studia Mathematica
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A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
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.
Stefano Meda (1989)
Rendiconti del Seminario Matematico della Università di Padova
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