Related papers: Inequalities in Fourier analysis on binary cubes

We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. For the additive version, we introduce Riccati pairs that…

We establish weighted Bernstein inequalities in $L^p$ space for the doubling weight on the conic surface $\mathbb{V}_0^{d+1} = \{(x,t): \|x\| = t, x \in \mathbb{R}^d, t\in [0,1]\}$ as well as on the solid cone bounded by the conic surface…

We introduce an analytic family of twisted Fourier transforms $\left\{\mathcal{F}^{(x)}_p\right\}_{x\in \mathbb{R},p\in [1,2)}$ for non-Kac compact quantum groups and establish a sharpened form of the Hausdorff-Young inequality in the range…

This paper is devoted to the refine analysis of Courant's theorem for the Dirichlet Laplacian. Many papers (and some of them quite recent) have investigated in which cases this inequality in Courant's theorem is an equality: Pleijel,…

We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…

Let $m(G)$ be the infimum of the volumes of all open subgroups of a unimodular locally compact group $G$. Suppose integrable functions $\phi_1 , \phi_2 \colon G \to [0,1]$ satisfy $\| \phi_1 \| \leq \| \phi_2 \|$ and $\| \phi_1 \| + \|…

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the…

This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…

Let $(X,\|\cdot\|_X)$ be a Banach space. The purpose of this article is to systematically investigate dimension independent properties of vector valued functions $f:\{-1,1\}^n\to X$ on the Hamming cube whose spectrum is bounded above or…

In this paper, we introduce new general frameworks for estimating the maximal dimension of Hilbert cubes contained in finite truncations of arbitrary sets. As applications, we investigate Hilbert cubes in a range of arithmetic sets,…

Our goal in this paper is to find a characterization of $n$-dimensional bilinear Hardy inequalities \begin{align*} \bigg\| \,\int_{B(0,\cdot)} f \cdot \int_{B(0,\cdot)} g \,\bigg\|_{q,u,(0,\infty)} & \leq C \, \|f\|_{p_1,v_1,{\mathbb R}^n}…

This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…

Let $\Omega\subset \mathbb{R}^N$ ($N\geq 3$) be an open domain which is not necessarily bounded. The sharp constant and extremal functions to the following kind of double-variable inequalities $$ S_{\alpha,\beta,\lambda,\mu}(\Omega)…

We prove that for any pair of i.i.d. random variables $X,Y$ with finite moment of order $a \in (0,2]$ it is true that $E |X-Y|^a \leq E |X+Y|^a$. Surprisingly, this inequality turns out to be related with bifractional Brownian motion. We…

An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…

In this paper, we derive some new combinatorial inequalities by applying well known real analytic results like H\"{o}lder's inequality, Young's inequality, and Minkowiski's inequality to the recursively defined sequence $f_n$ of functions…

An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…

If a pair of functions nearly extremizes Young's convolution inequality for R^d, with all three exponents finite and strictly greater than 1, then each function is close in norm to a Gaussian. The proof relies on the Riesz-Sobolev…

Let $f$ be a real-valued, degree-$d$ Boolean function defined on the $n$-dimensional Boolean cube $\{\pm 1\}^{n}$, and $f(x) = \sum_{S \subset \{1,\ldots,d\}} \widehat{f}(S) \prod_{k \in S} x_k$ its Fourier-Walsh expansion. The main result…

We derive a number of sharp upper bounds for the deficit in the Alexandrov-Fenchel inequality using a weighted Minkowski integral formula and an integral formula for the deficit in Jensen's inequality. Our estimates yield results under…