Related papers: Improved Stein inequalities for the Fourier transf…
This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…
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 a weighted version of the Hardy-Littlewood-Sobolev inequality for radially symmetric functions, and show that the range of admissible power weights appearing in the classical inequality due to Stein and Weiss can be improved in…
In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.
In this note we consider inequalities involving the error function $\phi$. Our methodes give new proofs of some known inequalities of Komatsu, and of Szarek and Werner, and also produce two families of inequalities that give upper and lower…
Using the Fourier transform, we obtain upper bounds for sums of eigenvalues of the free plate.
The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population…
In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined in $\R^d$ and observed in a bounded window. The procedure is based on a new general…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
This paper is a sequel of \cite{CD:2012}. We show how to establish a functional Edgeworth expansion of any order thanks to the Stein method. We apply the procedure to the Brownian approximation of compensated Poisson process and to the…
We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein-Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we…
Euler's inequality is a well known inequality relating the inradius and circumradius of a triangle. In Euclidean geometry, this inequality takes the form $R \geq 2r$ where $R$ is the circumradius and $r$ is the inradius. In spherical…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
We extend the classical Copson's inequalities so that the values of parameters involved go beyond what is currently known.
In this paper, we aim to establish a range of numerical radius inequalities. These discoveries will bring us to a recently validated numerical radius inequality and will present numerical radius inequalities that exhibit enhanced precision…
A Paley type inequality for the Fourier transform on $H^p(H^n);$ the Hardy space on the Heisenberg group, is obtained for $0 < p \leq 1.$