相关论文: Product kernels adapted to curves in the space

We study pointwise and $L^p$ gradient estimates of the heat kernel, on manifolds that may have some amount of negative Ricci curvature, provided it is not too negative (in an integral sense) at infinity. We also prove uniform boundedness…

We investigate the Hilbert transform and the maximal operator along a class of variable non-flat polynomial curves $(P(t),u(x)t)$ with measurable $u(x)$, and prove uniform $L^p$ estimates for $1<p<\infty$. In particular, via the change of…

A convolution operator in $\mathbb{R}^d$ with kernel in $L_q$ acts from $L_p$ to $L_s$, where $1/p+1/q=1+1/s$. The main theorem states that if $1<q,p,s<\infty$, then there exists an $L_p$ function of unit norm on which the $s$-norm of the…

We give a characterization of a variation of constants type estimate relating two positive semigroups on (possibly different) $L_p$-spaces to one another in terms of corresponding estimates for the respective generators and of estimates for…

We characterize the $L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions.

Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance…

We prove uniform $L^p \to L^q$ bounds for Fourier restriction to polynomial curves in $\mathbb R^d$ with affine arclength measure, in the conjectured range.

This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…

The purpose of this article is to introduce a new class of kernels on SO(3) for approximation and interpolation, and to estimate the approximation power of the associated spaces. The kernels we consider arise as linear combinations of…

The aim of this article is to give a complete solution to the problem of the bilinear decompositions of the products of some Hardy spaces $H^p(\mathbb{R}^n)$ and their duals in the case when $p<1$ and near to $1$, via wavelets, paraproducts…

In this paper, we investigate the trigonometric Heckman-Opdam polynomials of type $A_1$. We establish connections with ultraspherical polynomials and derive an explicit expression for the associated Poisson kernel. Using the product…

We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…

In this paper, we study the bilinear cone multiplier operator in two dimensions. We establish $L^{p_1}\times L^{p_2}\to L^{p}$ boundedness for a regularized version of this operator over a broad range of exponents satisfying the H\"older…

Let $p\in (1,\infty)$. In this paper, for any given measurable function $u:\ \mathbb{R}\rightarrow \mathbb{R}$ and a generalized plane curve $\gamma$ satisfying some conditions, the $L^p(\mathbb{R}^2)$ boundedness of the Hilbert transform…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Hypercontractivity is proved for products of qubit channels that belong to self-adjoint semigroups. The hypercontractive bound gives necessary and sufficient conditions for a product of the form e^{- t_1 H_1} \ot ... \ot e^{- t_n H_n} to be…

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…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.

Let $p\in [1,\infty)$. We define an $L^p$-operator algebra crossed product by a transfer operator for the topological Bernoulli shift $\varphi$ on $X=\{1,...,n\}^{\mathbb{N}}$, and we prove it is isometrically isomorphic to the $L^p$-analog…