Related papers: Bernstein type inequality in the shift-invariant s…
Two types of Bernstein inequalities are established on the unit ball in $\mathbb{R}^d$, which are stronger than those known in the literature. The first type consists of inequalities in $L^p$ norm for a fully symmetric doubling weight on…
In this paper, we establish separate necessary and sufficient John-Nirenberg (JN) type inequalities for functions in $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ which imply Gagliardo-Nirenberg (GN) type inequalities in…
Necessary and sufficient conditions are given for density of shift-invariant subspaces of the space $\mathcal{L}$ of integrable functions of bounded support with the inductive limit topology.
The purpose of this expository note is to give a proof of a Schur-type theorem that characterizes the inner functions in terms of their Taylor coefficients. In view of Beurling's theorem, this provides a sequential characterization of the…
We extend the classical Bernstein inequality to a general setting including Schr{\"o}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreover , we prove a new reverse inequality that can be seen…
In this paper we generalize the classical Nikol'skii inequality on the many popular classes pairs of rearrangement invariant (r.i.) spaces and construct some examples in order to show the exactness of our estimations.
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.
We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results show that the Bernstein inequality in a general…
We prove a reverse form of the multidimensional Brascamp-Lieb inequality. Our method also gives a new way to derive the Brascamp-Lieb inequality and is rather convenient for the study of equality cases.
We show that a Beurling type theory of invariant subspaces of noncommutative $H^2$ spaces holds true in the setting of subdiagonal subalgebras of $\sigma$-finite von Neumann algebras. This extends earlier work of Blecher and Labuschagne for…
By using Bernstein-type inequality we define analogs of spaces of entire functions of exponential type in $L_{p}(X), 1\leq p\leq \infty$, where $X$ is a symmetric space of non-compact. We give estimates of $L_{p}$-norms, $1\leq p\leq…
In this paper, inspired by the work of Da Lio-Rivi\`{e}re-Wettstein, we investigate the boundary-value characterizations of weighted Bergman spaces and establish a weighted Da Lio-Rivi\`{e}re-Wettstein inequality. In addition, we obtain…
This paper characterises the subspaces of $H^2(\mathbb D)$ simultaneously invariant under $S^2 $ and $S^{2k+1}$, where $S$ is the unilateral shift, then further identifies the subspaces that are nearly invariant under both $(S^2)^*$ and…
We summarize results concerning the Bernstein property of differential equations.
We prove in this article the generalizations on the exponential Orlicz spaces Markov's - Bernstein's inequalities for algebraic polynomials and rational functions.
We give an inequality of type sup+Cinf in dimension 2.
We establish an Azuma type inequality under a Lipshitz condition for martingales in the framework of noncommutative probability spaces and apply it to deduce a noncommutative Heoffding inequality as well as a noncommutative McDiarmid type…
In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…
Let $V$ be a symmetric convex body in $\R^m$. We prove sharp Bernstein-type inequalities for entire functions of exponential type with the spectrum in $V$ and discuss certain properties of the extremal functions. Markov-type inequalities…
In this paper we study the continuity of the Berezin transform on modified Bergman spaces and we establish a Lipschitz estimate in terms of the Bergman-Poincar\'e metric.