- 96-108 Netrusov Y., Weidl T.
- On Lieb-Thirring inequalities for higher order operators with
critical and subcritical powers
(47K, amslatex)
Mar 27, 96
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Abstract. Let e_k denote the negative eigenvalues of
the operator
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H_l(V)u:=(-Delta)^l u-V(x)u, V geq 0, x in R^d
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on L_2(R^d).
We prove the two-sided estimate
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A(d,l) int V(x)dx leq sum_k |e_k|^{1-q} leq B(d,l) int V(x)dx
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for q=d/2l<1.
We discuss bounds on the Riesz means sum_k |e_k|^p if 0<p<1-q.
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