Related papers: Cancellative sparse domination

The well known result of Bourgain and Kwapie\'n states that the projection $P_{\leq m}$ onto the subspace of the Hilbert space $L^2\left(\Omega^\infty\right)$ spanned by functions dependent on at most $m$ variables is bounded in $L^p$ with…

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…

Consider the discrete cubic Hilbert transform defined on finitely supported functions $f$ on $\mathbb{Z}$ by \begin{eqnarray*} H_3f(n) = \sum_{m \not = 0} \frac{f(n- m^3)}{m}. \end{eqnarray*} We prove that there exists $r <2$ and universal…

We prove weighted weak-type $(r,r)$ estimates for operators satisfying $(r,s)$ limited-range sparse domination of $\ell^q$-type. Our results contain improvements for operators satisfying limited-range and square function sparse domination.…

Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its type setting counterpart. We prove that…

In this article, we address pointwise sparse domination for multilinear Calder\'on-Zygmund operators on upper doubling, geometrically doubling metric measure spaces. As a consequence, we have obtained sharp quantitative weighted estimates…

We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of…

We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving $L^p$-averages. This class includes the adjoint forms to the bilinear Hilbert…

We give a short proof of the sharp weighted bound for sparse operators that holds for all $p$, $1<p<\infty$. By recent developments this implies the bounds hold for any Calder\'on-Zygmund operator. The novelty of our approach is that we…

In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-H\"ormander condition, then $T$ can be dominated by multilinear sparse operators.

We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…

Structural results impose sufficient conditions on the model parameters of a Markov decision process (MDP) so that the optimal policy is an increasing function of the underlying state. The classical assumptions for MDP structural results…

In this work we present a new approach to molecules on Goldberg's local Hardy spaces $h^p(\mathbb{R}^n)$, $0<p\leq1$, assuming an appropriate cancellation condition. As applications, we prove a version of Hardy's inequality and improved…

We consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on the integral norm discretization, we consider the absolute error setting. We demonstrate how known…

In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a…

Let (S_0,S_1,...) be a supermartingale relative to a nondecreasing sequence of \sigma-algebras (H_{\le0},H_{\le1},...), with S_0\le0 almost surely (a.s.) and differences X_i:=S_i-S_{i-1}. Suppose that for every i=1,2,... there exist…

In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…

Concerned with elliptic operators with stationary random coefficients governed by linear or nonlinear mixing conditions and bounded (or unbounded) $C^1$ domains, this paper mainly studies (weighted) annealed Calder\'on-Zygmund estimates,…

We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…