Related papers: Sparse Bounds for Oscillatory and Random Singular …

Given sparse collections of measurable sets $\mathcal S_k$, $k=1,2,\ldots ,N$, in a general measure space $(X,\mathfrak M,\mu)$, let $ \Lambda_{\mathcal S_k}$ be the sparse operator, corresponding to $\mathcal S_k$. We show that the maximal…

Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…

The purpose of this paper is to study algebras of singular integral operators on $\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\'on-Zygmund operators with different homogeneities, such as…

In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…

Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…

We investigate the boundedness of oscillating singular integrals on Lie groups of polynomial growth in order to extend the classical oscillating conditions due to Fefferman and Stein for the boundedness of oscillating convolution operators.…

The problem of CSP sparsification asks: for a given CSP instance, what is the sparsest possible reweighting such that for every possible assignment to the instance, the number of satisfied constraints is preserved up to a factor of $1 \pm…

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…

We study the extent of independence needed to approximate the product of bounded random variables in expectation, a natural question that has applications in pseudorandomness and min-wise independent hashing. For random variables whose…

Let $T_\Omega$ be the singular integral operator with variable kernel $\Omega(x,z)$. In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of $T_\Omega$ on these…

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient…

We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + \lambda x^{\otimes p}$ with $\pmb W \in \otimes^p\mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit…

We use Cram\'er-Chernoff type estimates in order to study the Calder\'on-Zygmund structure of the kernels $\sum_{I\in\mathcal{D}}a_I(\omega)\psi_I(x)\psi_I(y)$ where $a_I$ are subgaussian independent random variables and $\{\psi_I:…

An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of…

We improve an $L^2\times L^2\to L^2$ estimate for a certain bilinear operator in the finite field of size $p$, where $p$ is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a…

This paper present an overview of some of the applications of the martingale inequalities of D.L. Burkholder to $L^p$-bounds for singular integral operators, concentrating on the Hilbert transform, first and second order Riesz transforms,…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Motivated by the recent works [Huan Yu, Quansen Jiu, and Dongsheng Li, 2021] and [Yanping Chen and Zihua Guo, 2021], we study the following extension of Calder\'on-Zygmund type singular integrals $$ T_{\beta}f (x) = p.v. \int_{\mathbb{R}^n}…

In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…

We prove that for all p>1/2 there exists a constant $\gamma_p>0$ such that, for any symmetric measurable set of positive measure $E\subset \TT$ and for any $\gamma<\gamma_p$, there is an idempotent trigonometrical polynomial f satisfying…