Some properties of fractional integrals. II.
G. H., and J.E.Littlewood, Hardy (1932)
Mathematische Zeitschrift
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G. H., and J.E.Littlewood, Hardy (1932)
Mathematische Zeitschrift
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John Steinig (1970)
Mathematische Zeitschrift
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Roop Narain Kesarwani (1967)
Mathematische Zeitschrift
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Miroslav Pavlović (1996)
Publications de l'Institut Mathématique
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R.K. Saxena (1967)
Mathematische Zeitschrift
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Gurka, Petr, Opic, Bohumír (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Roop Narain Kesarwani (1968)
Mathematische Zeitschrift
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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.
Krishna Ji Srivastava (1957)
Mathematische Zeitschrift
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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.
Branislav Martić (1973)
Publications de l'Institut Mathématique
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