Hardy inequalities for fractional integrals on general domains
By Michael Loss, Craig A. Sloane. 2009
92 citations recorded by the source corpus.
We prove a sharp Hardy inequality for 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.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/99f406f7901126e9570ab2552e5f570faffd7e17
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In Applied Mathematics
- Antti V. Vahakangas
- Bartłomiej Dyda
- Rupert L. Frank
- Hichem Hajaiej
- Zhichun Zhai
- Xinwei Yu
- Ariel Martin Salort
- Robert Seiringer
In Numerical Analysis
Citations in the corpus
- The best constant in a fractional Hardy inequality (2008, unknown): “In fact, in the paper [9] a much more general result than Theorem 1 was obtained.”
- A framework for fractional Hardy inequalities (2013, background): “In another direction, the sharp constants for fractional Hardy-type inequalities on general domains are obtained in [27], where the distance is replaced with an averaged pseudo distance.”
- 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.”
- 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].”
- Fractional Hardy-Sobolev-Maz'ya inequality for domains (2011, methodology): “In the last section, we extend the method developed in [8] and use results from [11] and [13] to prove Theorem 1.”