Related papers: $L_p$-norm spherical copulas

In this paper, given a prescribed measure on $\mathbb{S}^1$ whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar $L_p$ dual Minkowski problem when $0<p<1$ and $q\ge 2$. We also prove…

In this survey, we collect recent progress in the understanding of $L^{p}$ bounds for bilinear spherical averages and some associated maximal functions like the bilinear spherical maximal function and its lacunary counterpart. We describe…

For any $p\in[1,\infty]$, we prove that the set of simple functions taking at most $k$ different values is proximinal in $L^p$ for all $k\geq 1$. We introduce the class of uniformly approximable subsets of $L^p$, which is larger than the…

We examine sets $\mathscr A$ of natural numbers having the property that for some real number $p\in (0,2)$, one has the subconvex bound $$\int_0^1 \Bigl| \sum_{n\in \mathscr A\cap [1,N]}e(n\alpha)\Bigr|^p\, {\rm d}\alpha \ll N^{-1}|\mathscr…

We give a simple explicit description of the norm in the complex interpolation space $(C_p[L_p(M)], R_p[L_p(M)])_\theta$ for any von Neumann algebra $M$ and any $1\le p\le\infty$.

We study $L^p$ boundedness of the maximal average over dilations of a smooth hypersurface $S$. When the decay rate of the Fourier transform of a measure on $S$ is $1/2$, we establish the optimal maximal bound, which settles the conjecture…

This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…

We establish the $L_p$-regularity theory for a semilinear stochastic partial differential equation with multiplicative white noise: $$ du = (a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + \bar b^{i}|u|^\lambda u_{x^i})dt + \sigma^k(u)dw_t^k,\quad…

Consider the wave equation associated with the Kohn Laplacian on groups of Heisenberg type. We construct parametrices using oscillatory integral representations and use them to prove sharp $L^p$ and Hardy space regularity results.

We prove that for a finite type curve in $\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \to L^{p}_{1/p}$ regularity result for the averaging operators…

In this paper, which is a sequel to math.DG/9902111, we analyze the limit of the p-form Laplacian under a collapse with bounded sectional curvature and bounded diameter to a singular limit space. As applications, we give results about upper…

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian, and to the boundedness of $L^p$ norms of eigenfunctions of the…

We consider the spaces $A_p(\mathbb T)$ of functions $f$ on the circle $\mathbb T$ such that the sequence of Fourier coefficients $\fu{\f}=\{\fu{\f}(k), ~k \in \mathbb Z\}$ belongs to $l^p, ~1\leq p<2$. The norm on $A_p(\mathbb T)$ is…

In this paper, we prove the propagation of $L^p$ upper bounds for the spatially homogeneous relativistic Boltzmann equation for any $1<p<\infty$. We consider the case of relativistic \textit{hard ball} with Grad's angular cutoff. Our proof…

In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure…

We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal…

Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…

We show that, for every $1 \leq p < +\infty$ and for every Borel probability measure $\mathbb{P}$ over $\mathbb{R}$, every element of $L^{p}(\mathbb{R}, \mathscr{B}_{\mathbb{R}}, \mathbb{P})$ is the $L^{p}$-limit of some sequence of bounded…

We derive sparse bounds for the bilinear spherical maximal function in any dimension $d\geq 1$. When $d\geq 2$, this immediately recovers the sharp $L^p\times L^q\to L^r$ bound of the operator and implies quantitative weighted norm…

We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sq^n in Sp(lq^m) with optimal order m = n^2.…