Related papers: Variational inequalities for bilinear averages
Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…
We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and…
In this paper, we establish some new general Opial inequalities for Widder derivatives.
The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…
We prove mean convergence, as $N\to\infty$, for the multiple ergodic averages $\frac{1}{N}\sum_{n=1}^N f_1(T_1^{p_1(n)}x)... f_\ell(T_\ell^{p_\ell(n)}x)$, where $p_1,...,p_\ell$ are integer polynomials with distinct degrees, and…
In the first part of the paper the natural scheme for proving noncommutative individual ergodic theorems for multiple sequences is described and applied to obtain results on unrestricted convergence of multiaverages. In the second part…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
We prove, in a unified way, $r$-variational estimates, $r>2$, on $\ell^{s}(\mathbb{Z})$ spaces, $s \in (1, \infty)$, for averages and truncated singular integrals along the set of prime numbers.
We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\neq j$. The limiting behavior of such…
Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to…
In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of…
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
In this paper we study the mapping properties of the averaging operator over a variety given by a system of homogeneous equations over a finite field. We obtain optimal results on the averaging problems over two dimensional varieties whose…
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…