Related papers: Young's integral inequality with upper and lower b…
We prove some extensions of Andrews inequality.
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings or measurement outcomes. In this article, such "liftings" of Bell inequalities are…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are…
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…
An unconditional inequality of the totient function is contributed to the literature. This result is associated with various problems about the distribution of prime numbers.
Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or R\'enyi entropies. The proof is based on a…
We review several aspects of Yang-Mills theory (YMT) in two dimensions, related to its perturbative and topological properties. Consistency between light-front and equal-time formulations is thoroughly discussed.
In this paper, we establish some integral ineuqalities for n- times differentiable convex functions.
Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Lo\'{e}ve-Young inequality for the…
This paper studies two classical inequalities, namely the Hausdorff-Young inequality and equal-exponent Young's convolution inequality, for discrete functions supported in the binary cube $\{0,1\}^d\subset\mathbb{Z}^d$. We characterize the…
We explore inequality constraints as a new tool for numerically evaluating Feynman integrals. A convergent Feynman integral is non-negative if the integrand is non-negative in either loop momentum space or Feynman parameter space. Applying…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant $\delta$. The bound is expressed in the uniform entropy integral of…
We consider the variance of a function of $n$ independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d.~setting. For instance, we obtain various…
We prove the stronger version of Harnack's inequality for positive harmonic functions defined on the unit disc.
In this paper, new sharp bounds for circular functions are proved. We provide some improvements of previous results by using infinite products, power series expansions and a generalisation of the so-called Bernoulli inequality. New proofs,…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.
We present a new Aumann-like integral for a H\"older multifunction with respect to a H\"older signal, based on the Young integral of a particular set of H\"older selections. This restricted Aumann integral has continuity properties that…