Related papers: Variational inequalities for bilinear averages

An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…

This article is devoted to the study of the historic set of ergodic averages in some nonuniformly hyperbolic systems. In particular, our results hold for the robust classes of multidimensional nonuniformly expanding local diffeomorphisms…

It is shown that there exist a subsequence for which the multiple ergodic averages of commuting invertible measure preserving transformations of a Lebesgue probability space converge almost everywhere provided that the maps are weakly…

In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially answering questions posed by the first author, Maass and the…

We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.

We examine the convergence of ergodic averages along polynomials in Toeplitz systems and prove that it is possible for averages along one polynomial to converge, and along another to diverge. We also study density of the polynomial orbits…

In this paper, we establish a noncommutative analogue of Calder\'on's transference principle, which allows us to deduce noncommutative ergodic maximal inequalities from the special case---operator-valued maximal inequalities. As…

Exploiting the recent work of Tao and Ziegler on a concatenation theorem on factors, we find explicit characteristic factors for multiple averages along polynomials on systems with commuting transformations, and use them to study criteria…

We obtain generalized Wintgen inequalities for submanifolds in conformally flat manifolds. We give some applications for submanifolds in a Riemannian manifold of quasi-constant curvature. Equality cases are also considered.

We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient…

We show that a $k$-linear pointwise ergodic theorem on an ergodic measure-preserving system implies a uniform $k$-linear nilsequence Wiener-Wintner theorem on that system. The assumption is known to hold for arbitrary systems and $k=2$ (due…

We establish a quantitative weighted inequality for the bilinear rough singular integral, where the bound is controlled by the cube of the weight constant.

We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly…

In this paper, we extend the generalized Wiener-Wintner Theorem built by Host and Kra to the multilinear case under the hypothesis of pointwise convergence of multilinear ergodic averages. In particular, we have the following result: Let…

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables

Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…

We show slow convergence of weighted ergodic averages for flows and actions of countable amenable groups.

We obtain simple proofs of certain inequalites for bivariate means.

We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…