Related papers: Continuous sparse domination and dimensionless wei…

We present a new proof of the dimensionless $L^p$ boundedness of the Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion, namely that of a new dimensionless…

We develop the self similarity argument known as sparse domination in an abstract martingale setting, using a continuous time parameter. With this method, we prove a sharp weighted L^p estimate for the maximal operator Y^* of Y with respect…

We prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition…

We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To…

We extend Lerner's recent approach to sparse domination of Calder\'on--Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure spaces. Our domination theorem is different from the one…

We present a general approach to sparse domination based on single-scale $L^p$-improving as a key property. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic…

We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…

We prove a sharp dimensionless weighted estimate of the Riesz vector on a Riemannian manifold with non-negative Bakry-Emery curvature. The proof is by the method of Bellman functions, where the explicit expression of a Bellman function of…

By means of appropriate sparse bounds, we deduce compactness on weighted $L^p(w)$ spaces, $1<p<\infty$, for all Calder\'on-Zygmund operators having compact extensions on $L^2(\mathbb{R}^n)$. Similar methods lead to new results on…

The technique of sparse domination, i.e., dominating operators with sums of averages taken over sparsely distributed cubes, has seen rapid development recently within the realms of harmonic analysis. A useful extension of sparse domination…

We provide a versatile formulation of Lacey's recent sparse pointwise domination technique with a local weak type estimate on a nontangential maximal function as the only hypothesis. We verify this hypothesis for sharp variational…

We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from $\mathbf{R}^n$ to the half-space in $\mathbf{R}^{1+n}$ above $\mathbf{R}^n$. The proof is based on pointwise sparse…

In this paper, we study maximal functions along some finite type curves and hypersurfaces. In particular, various impacts of non-isotropic dilations are considered. Firstly, we provide a generic scheme that allows us to deduce the sparse…

We prove a local two-weight Poincar\'e inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman--Stein inequality for the sharp maximal…

We prove a quadratic sparse domination result for general non-integral square functions $S$. That is, we prove an estimate of the form \begin{equation*} \int_{M} (S f)^{2} g \, \mathrm{d}\mu \le c \sum_{P \in \mathcal{S}}…

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 prove a general sparse domination theorem in a space of homogeneous type, in which a vector-valued operator is controlled pointwise by a positive, local expression called a sparse operator. We use the structure of the operator to get…

Convex body domination is an important elaboration of the technique of sparse domination that has seen significant development and applications over the past ten years. In this paper, we present an abstract framework for convex body…

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be feasible. As a consequence of…

The goal of this expository paper is to give a self-contained introduction to sparse domination. This is a method relying on techniques from dyadic Harmonic Analysis which has received a lot of attention in recent years. Essentially, it…