312 research outputs found
Hardy inequalities for fractional integrals on general domains
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.Comment: LaTeX, 9 pages, a number of errors have been fixed and the
bibliography has been update
A simple proof of a theorem of Laptev and Weidl
A new and elementary proof of a recent result of Laptev and Weidl is given.
It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger
operators with matrix valued potentials.Comment: Replaces the version of June 28, 1999. A technical error in the proof
has been correcte
Hardy-Sobolev-Maz'ya inequalities for arbitrary domains
We prove a Hardy-Sobolev-Maz'ya inequality for arbitrary domains
\Omega\subset\R^N with a constant depending only on the dimension N\geq 3. In
particular, for convex domains this settles a conjecture by Filippas, Maz'ya
and Tertikas. As an application we derive Hardy-Lieb-Thirring inequalities for
eigenvalues of Schr\"odinger operators on domains.Comment: 19 page
Lieb-Thirring inequalities with improved constants
Following Eden and Foias we obtain a matrix version of a generalised Sobolev
inequality in one-dimension. This allow us to improve on the known estimates of
best constants in Lieb-Thirring inequalities for the sum of the negative
eigenvalues for multi-dimensional Schroedinger operators
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