Related papers: Noncommutative weak Orlicz spaces and martingale i…

We prove disjointification inequalities due to Johnson and Schechtman for noncommutative random variables independent in the sense of Junge and Xu. In the same setting, we also prove noncommutative Khinchine inequalities. These inequalities…

In this paper we describe the notion of a weak lipschitzianity of a mapping on a $C^{q}$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly…

We give a criterion for the weak convergence of unit Borel measures on the N-dimensional Berkovich projective space over a complete non-archimedean field. As an application, we give a sufficient condition for equidistribution in terms of a…

In this paper we study an extension problem for the Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type and use the solution to prove Hardy-type inequalities for fractional powers of the Laplace-Beltrami operator.…

We compute numerically the $L^2$ Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test some relevant rules on domains such as the interval, the…

Let G be a locally compact abelian group, $\omega:G\to (0,\infty)$ be a weight, and ($\Phi$,$\Psi$) be a complementary pair of strictly increasing continuous Young functions. We show that for the weighted Orlicz algebra $L^\Phi_\omega(G)$,…

We compute the K-functional related to some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces completing the results of the previous works of the authors. This computation allows to determine the…

We investigate well-posedness for martingale solutions of stochastic differential equations, under low regularity assumptions on their coefficients, widely extending some results first obtained by A. Figalli. Our main results are a very…

The aim of this paper is to begin a systematic study of functional inequalities on symmetric spaces of noncompact type of higher rank. Our first main goal of this study is to establish the Stein-Weiss inequality, also known as a weighted…

Let X be a Banach space. We prove p-independence of the one-sided decoupling inequality for X-valued tangent martingales as introduced by Kwapien and Woyczynski. It is known that a Banach space X satisfies the two-sided decoupling…

We give a proof of the Khintchine inequalities in non-commutative $L_p$-spaces for all $0< p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, e.g. for the…

We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…

We prove capacitary strong type inequalities for functions belonging to Orlicz-Sobolev spaces. As an application we consider capacitary averages and their limits.

We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the non-sharp admissible region of exponents, covering wave, Klein-Gordon, and fractional Schr\"odinger equations. Our approach combines the…

In the present paper, we prove that a lower bound on the $1$-weighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the…

In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class…

For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted $L^p$ space is given. The result is then used to…

In this note we extend several integral inequalities to the context of noncommutative Vilenkin groups. We prove some sharp weak and strong type estimates for the Hardy operator and the Hardy-Littlewood-P{\'o}lya operator on constant-order…

In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foias, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative…