Related papers: Weighted Norm Estimates and Representation Formula…
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…
This paper is motivated by Phong and Stein's paper on non-standard singular integrals with mixed homogeneities. Our purpose is to study these new non-standard convolution singular integrals and establish the boundedness of these singular…
Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
The main aim of this article is to establish boundedness of singular integrals with non-smooth kernels on product spaces. Let $L_1$ and $L_2$ be non-negative self-adjoint operators on $L^2(\mathbb{R}^{n_1})$ and $L^2(\mathbb{R}^{n_2})$,…
This paper deals with the weak error estimates of the exponential Euler method for semi-linear stochastic partial differential equations (SPDEs). A weak error representation formula is first derived for the exponential integrator scheme in…
We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to…
In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually…
This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear…
We obtain some "universal" estimates for $L_2$-norm of the solution of a parabolic equation via a weighted version of $H^{-1}$-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation…
Consider the following nonlinear elliptic equation of $p(x)$-Laplacian type with nonstandard growth \begin{equation*} \left\{ \begin{aligned} &{\rm div} a(Du, x)=\mu \quad &\text{in}& \quad \Omega, &u=0 \quad &\text{on}& \quad…
We prove a new dyadic representation theorem with applications to the $T(1)$ and $A_2$ theorems. In particular, we obtain the non-homogeneous $T(1)$ theorem under weaker kernel regularity than the earlier approaches.
The $L^p$ ($1<p<\infty$) and weak-$L^1$ estimates for the variation for Calder\'on-Zygmund operators with smooth odd kernel on uniformly rectifiable measures are proven. The $L^2$ boundedness and the corona decomposition method are two key…
We address the problem of estimating the edge of a bounded set in R^d given a random set of points drawn from the interior. Our method is based on a transformation of estimators dedicated to uniform point processes and obtained by smoothing…
We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities of a class of one-sided oscillatory singular integrals with smooth kernel.
Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…
By bivariate irreducible representations of ${\rm Sp}(2r)$, we mean irreducible representations with highest weights containing at most two nonzero entries, using the usual identification of dominant weights for complex symplectic Lie…