We prove that the best constant in the general Brascamp–Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp–Lieb inequality which have arisen recently in harmonic analysis.

where V+ = (|V |+ V )/2 is the positive part of V . Eden and Foias have obtained in [3] a version of a one-dimensional generalised Sobolev inequality which gives best known estimates for the constants in the inequality (2) for 1 ≤ γ < 3/2. The aim of this short article is to extend the method from [3] to a class of matrix-valued potentials. By using ideas from [6] this automatically improves on...

We show that the lower and upper Frechét-Hoeffding copulas, which are singular, can be regularized to absolutely continuous copulas. The method, which is constructive and explicit, states sufficient conditions for when an absolutely continuous copula can be achieved by averaging. A higher degree of regularisation cannot be achieved with the proposed method.

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Bounds on test sequence length can be used as a testability measure. We give a procedure to compute the upper bound on test sequence length for an arbitrary sequential circuit. We prove that the bound is exact for a certain class of circuits. Three design rules are specified to yield circuits with lower test sequence bounds.

This article contains a method to bound the test errors of voting committees with members chosen from a pool of trained classifiers. There are so many prospective committees that validating them directly does not achieve useful error bounds. Because there are fewer classifiers than prospective committees, it is better to validate the classifiers individually than use linear programming to infer...

Let A and B be positive semidefinite matrices. We investigate the conditions under which the Lieb-Thirring inequality can be extended to singular values. That is, for which values of p does the majorisation σ(BpAp) ≺w σ((BA) p) hold, and for which values its reversed inequality σ(BpAp) ≻w σ((BA) p).

We give a short proof of the Cwikel–Lieb–Rozenblum (CLR) bound on the number of negative eigenvalues of Schrödinger operators. The argument, which is based on work of Rumin, leads to remarkably good constants and applies to the case of operator-valued potentials as well. Moreover, we obtain the general form of Cwikel’s estimate about the singular values of operators of the form f(X)g(−i∇).

We use `p estimates together with Brascamp-Lieb inequalities to obtain bounds on the variance of the solution u" to the elliptic equation r" a(x="; ')r"u" = r" f . The variance is shown to be O("r) where the exponent r depends on the contrast of a(x; '). In two dimensions, we show that variance of the Greens function of the above elliptic operator is bounded. We also obtain decay rates for the ...