Related papers: A note on the Menchov-Rademacher Inequality
We prove a multivariate version of Hoeffding's inequality about the distribution of homogeneous polynomials of Rademacher functions. The proof is based on such an estimate about the moments of homogeneous polynomials of Rademacher functions…
We review some results about quantitative improvements of sharp inequalities for eigenvalues of the Laplacian.
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
We analyze solutions of the Toda system and establish an optimal Moser-Trudinger inequality
Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
The aim of this paper is to construct a new expansion of $(1+1/x)^x$ related to Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001) 651-659].
Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…
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,…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli-Kohn-Nirenberg inequality. In three dimensions, in certain cases the sharp constant…
We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…
We prove that in the context of general Markov semigroups Beckner inequalities with constants separated from zero as $p\to 1^+$ are equivalent to the modified log Sobolev inequality (previously only one implication was known to hold in this…
Redheffer's inequality and its extensions are applied to study the behavior and estimates of the first eigenvalue of $p$-Laplacian with respect to $p$. Furthermore, a Redheffer-type inequality for the generalized trigonometric function is…
We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.
The Menchov-Rademacher inequality is an inequality in harmonic analysis that bounds the $L_2$ norm of a certain maximal operator. It was first established in order to prove almost everywhere convergence of a one-parameter series of…
We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.
\begin{abstract} Let $P\pm$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider estimates of the expression $\|( |P_ + f | ^s + |P_- f |^s) ^{\frac{1}{s}}\|_{L^p (\mathbf{T})}$ in terms of Lebesgue $p$-norm of the…
We present a short proof of a conjecture proposed by I. Ra\c{s}a (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the letter to I. Ra\c{s}a (2017). The methods of our proof…