Related papers: Discrete maximal operators and pinned simplices

Results analogous to those proved by Rubio de Francia are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators of limited decay. We focus our attention to $L^2\times L^2\to L^1$ estimates. We…

This note presents an example of an increasing sequence $(\lambda_l)_{l=1}^\infty$ such that the maximal operators associated to normalized discrete spherical convolution averages \[ \sup_{l\geq…

We provide some new estimates for Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal…

We obtain $L^p$ estimates of the maximal Schr\"odinger operator in $\mathbb R^n$ using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.

A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator (MLE) is a retraction from that simplex onto the model. We characterize all models for which this retraction is a rational function. This is…

We precisely evaluate Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to local Lorentz type estimates. Using a type of symmetrization principle, introduced for the dyadic…

In this article, we study discrete maximal function associated with the Birch-Magyar averages over sparse sequences. We establish sparse domination principle for such operators. As a consequence, we obtain $\ell^p$-estimates for such…

We consider a type of maximal operators associated to moment curves in $\mathbb R^d, d\geq 3.$ We derive $L^p$ mapping properties for these operators. In a special case, the estimate is sharp.

Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.

Consider the discrete maximal function acting on $\ell^2(\mathbb Z)$ functions \[ \mathcal{C}_{\Lambda} f( n ) := \sup_{ \lambda \in \Lambda} \left| \sum_{m \neq 0} f(n-m) \frac{e^{2 \pi i\lambda m^2}} {m} \right| \] where $\Lambda \subset…

We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.

Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…

The main aims of this article are to characterize a class of operators associated with the symmetrized polydisc that admit rational dilations on the minimal space and to show an interplay between rational dilation and distinguished…

We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth…

We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a…

We initiate the theory of $\ell^p$-improving inequalities for arithmetic averages over hypersurfaces and their maximal functions. In particular, we prove $\ell^p$-improving estimates for the discrete spherical averages and some of their…