Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1 ... s ... n/p.
Winfried Sickel (1997)
Forum mathematicum
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Winfried Sickel (1997)
Forum mathematicum
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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.
Hans-Gerd Leopold (1991)
Forum mathematicum
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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.
Wen Yuan, Yufeng Lu, Dachun Yang (2015)
Studia Mathematica
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In this article, via fractional Hajłasz gradients, the authors introduce a class of fractional Hajłasz-Morrey-Sobolev spaces, and investigate the relations among these spaces, (grand) Morrey-Triebel-Lizorkin spaces and Triebel-Lizorkin-type spaces on both Euclidean spaces and RD-spaces.
Gurka, Petr, Opic, Bohumír (2008)
Banach Journal of Mathematical Analysis [electronic only]
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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)].
Stefano Meda (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Yong-Kum Cho, Joonil Kim (2006)
Studia Mathematica
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As a natural extension of Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.
Der-Chen Chang (1994)
Forum mathematicum
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Tonia Ricciardi, Takashi Suzuki (2014)
Journal of the European Mathematical Society
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Yong-Kum Cho (2005)
Colloquium Mathematicae
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We prove Strichartz's conjecture regarding a characterization of Hardy-Sobolev spaces.
Steven G. Krantz (1979)
Mathematische Annalen
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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.
Klaus Gero Kalb (1984)
Mathematische Annalen
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Balinsky, A., Evans, W.D., Hundertmark, D, Lewis, R.T. (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Yoshihiro Sawano (2010)
Studia Mathematica
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The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.