Bounds for Strengthened Hardy and Polya-Knopp's Differences

On a strengthened Hardy-Hilbert type inequality

*Correspondence: [email protected] 2Department of Construction and Information Engineering, Guangxi Modern Vocational Technology College, Hechi, Guangxi 547000, China Full list of author information is available at the end of the article Abstract We derive a strengthenment of a Hardy-Hilbert type inequality by using the Euler-Maclaurin expansion for the zeta function and estimating the weight...

On a strengthened Hardy-Hilbert’s type inequality

In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive a strengthenment of a Hardy-Hilbert’s type inequality proved by W.Y. Zhong. As applications, some particular results are considered.

On further strengthened Hardy-Hilbert's inequality

Strengthened semidefinite programming bounds for codes

We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte ...

Hardy Spaces for Semigroups with Gaussian Bounds

Let Tt = e−tL be a semigroup of self-adjoint linear operators acting on L(X,μ), where (X, d, μ) is a space of homogeneous type. We assume that Tt has an integral kernel Tt(x, y) which satisfies the upper and lower Gaussian bounds: C1 μ(B(x, √ t)) exp ( −c1d(x, y)/t ) ≤ Tt(x, y) ≤ C2 μ(B(x, √ t)) exp ( −c2d(x, y)/t ) . By definition, f belongs to H L if ‖f‖H1 L = ‖ supt>0 |Ttf(x)|‖L1(X,μ) < ∞. W...