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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Gurka, Petr, Opic, Bohumír (2008)
Banach Journal of Mathematical Analysis [electronic only]
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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.
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.
M. Jevtić (1982)
Matematički Vesnik
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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.
B. Martić (1964)
Matematički Vesnik
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Masayoshi Hata (2005)
Acta Arithmetica
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Helena Musielak (1973)
Colloquium Mathematicae
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Öğünmez, Hasan, Özkan, Umut Mutlu (2011)
Journal of Inequalities and Applications [electronic only]
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Stefano Meda (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Lou, Zengjian (1994)
International Journal of Mathematics and Mathematical Sciences
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Pei-Luan Li, Chang-Jin Xu (2015)
Open Mathematics
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In this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.