Related papers: H\"older's inequality: some recent and unexpected …

The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…

The Bohr phenomenon for analytic functions of the form $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r_{f}$, $0<r_{f}<1$, such that the inequality $\sum_{n=0}^{\infty}…

We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality.…

Recently, many surveys are devoted to study the Clifford Fourier transform. Dealing with the real Clifford Fourier transform introduced by Hitzer [10], we establish analogues of the classical Heisenberg's inequality and Hardy's theorem in…

We give a variant of Weyl's inequality for systems of forms together with applications. First we use this to give a different formulation of a theorem of B. J. Birch on forms in many variables. More precisely, we show that the dimension of…

The Hardy--Littlewood inequalities for $m$-linear forms on $\ell_{p}$ spaces are known just for $p>m$. The critical case $p=m$ was overlooked for obvious technical reasons and, up to now, the only known estimate is the trivial one. In this…

Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.

A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…

This is a preprint of 1992 with some updates. We study sections of the exponential function Taylor series. Interesting inequalities for these sections were considered by G.Hardy, Kesava Menon, W. Gautschi, H.Alzer and others. The main aim…

We investigate improved forms of the Bohr inequality, using the quantity $S_r/\pi$, for analytic selfmaps in class $\mathcal{B}$ of $\mathbb{D}$, where $S_r$ is the area measure of $\mathbb{D}_r$. We then generalize the inequality for…

Classical boundary Hardy inequality, that goes back to 1988, states that if $1 < p < \infty, \ ~\Omega$ is bounded Lipschitz domain, then for all $u \in C^{\infty}_{c}(\Omega)$, $$\int_{\Omega} \frac{|u(x)|^{p}}{\delta^{p}_{\Omega}(x)} dx…

Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…

By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-P\'olya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using…

We use H\"older's inequality to get simple derivations of certain economic formulas involving CES, Armington, or $n$-stage Armington functions.

We show that generic H\"older continuous functions are $\rho$-irregular. The property of $\rho$-irregularity has been first introduced by Catellier and Gubinelli (Stoc. Proc. Appl. 126, 2016) and plays a key role in the study of…

Recently, there has been a number of good deal of research on the Bohr's phenomenon in various setting including a refined formulation of his classical version of the inequality. Among them, in \cite{PaulPopeSingh-02-10} the authors…

We give an historical account, including recent progress, on some problems of Erd\H os in number theory.

The main purpose of this article is to survey on some key elements of a recent $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n e^{-\lambda_{n}s}$, which was mainly inspired by the work of Bayart and Helson on ordinary Dirichlet…

In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is…

Let $ \mathcal{H}(\Omega) $ be the class of complex-valued functions harmonic in $ \Omega\subset\mathbb{C} $ and each $f=h+\overline{g}\in \mathcal{H}(\Omega)$, where $ h $ and $ g $ are analytic. In the study of Bohr phenomenon for certain…