Related papers: On Decoupling of Functions of Normal Vectors II

A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.

In this work we derive some inequalities for fractional boundary value problems, that generalize the well-known de la Vall\'ee Poussin inequality. With our results we also were able to improve the intervals where some Mittag-Leffler…

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

We obtain some new inequalities of Chebyshev Type.

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These…

We present an improved version of the second order Gaussian Poincar\'e inequality, firstly introduced in Chatterjee (2009) and Nourdin, Peccati and Reinert (2009). These novel estimates are used in order to bound distributional distances…

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…

In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.

Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y))…

The main objective of this paper is to obtain some Gruss Like Inequalities using Pompeiu's mean value theorem on Conformable Fractional Calculus.

We prove sharp $\ell^q L^p$ decoupling inequalities for $p,q \in [2,\infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for quadratic forms are also explained. We also include some…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

In this paper we prove a version of Gruss integral inequality for mappings with values in Hilbert C*-modules. Some applications for such functions are also given.

In this paper we establish some new inequalities of Hadamard-type for product of convex and s-convex functions in the second sense.

We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values…

The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…

Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.