The best constant in a fractional Hardy inequality
By Krzysztof Bogdan, Bartłomiej Dyda. 2008
119 citations recorded by the source corpus.
We prove an optimal Hardy inequality for the fractional Laplacian on the half‐space. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/f241d1827d5af52058a7b25361dde6567602d70e
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In Applied Mathematics
- Bartłomiej Dyda
- Lorenzo Brasco
- Ariel Martin Salort
- Rupert L. Frank
- Antti V. Vahakangas
- Bartłlomiej Dyda
- Hichem Hajaiej
- Zhichun Zhai
In Computational Theory and Mathematics
- Ariel Martin Salort
- Bartłlomiej Dyda
- Lorenzo Brasco
- Zhichun Zhai
- Xinwei Yu
- Hichem Hajaiej
- Craig A. Sloane
- Michael Loss
Citations in the corpus
- Fractional Hardy-Sobolev-Maz'ya inequality for domains (2011, background): “Γ ( N+2s 2 ) B(1+2s 2 , 1− s)− 22s 22s+1s = 2κN,2s, where κN,2s is the notation used in [3, 13, 6].”
- Fractional calculus for power functions and eigenvalues of the fractional Laplacian (2012, result): “Lower bounds for eigenvalues Our approach to lower bounds is similar to that of [11].”
- Eigenvalues and minimizers for a non-standard growth non-local operator (2018, background): “In fractional spaces see for instance [5, 26, 31] and references to these papers.”
- Convexity properties of Dirichlet integrals and Picone-type inequalities (2014, background): “Other fractional Hardy inequalities have appeared in the literature, see [6, 15].”
- Fractional calculus for power functions and eigenvalues of the fractional Laplacian (2012, result): “Lower bounds for eigenvalues Our approach to lower bounds is similar to that of [11].”
- A framework for fractional Hardy inequalities (2013, background): “In [9] these results are further refined; let us also mention the other related papers [4, 8, 11, 12, 34].”
- Fractional Gagliardo–Nirenberg and Hardy inequalities under Lorentz norms (2012, methodology): “The fractional Hardy inequalities under Lebesgue norms have been extensively studied by Bogdan and Dyda [28], Dyda [29], Frank and Seiringer [30], Loss and Sloane [31], and Ostrovsky and Sirota [32].”
- Hardy inequalities for fractional integrals on general domains (2009, result): “r fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda [2]. 1. Introduction In this note we prove a conjecture of Bogdan and Dyda [2] concerning Hardy ineq”