Related papers: Sparse bounds for maximal rough singular integrals…

We show, using a Knapp-type homogeneity argument, that the $(L^p, L^2)$ restriction theorem implies a growth condition on the hypersurface in question. We further use this result to show that the optimal $(L^p, L^2)$ restriction theorem…

In this work, we establish $L^{p_1}\times \cdots\times L^{p_m}\to L^p$ bounds for maximal multi-(sub)linear singular integrals associated with homogeneous kernels $\frac{\Omega(\vec{\boldsymbol{y}}')}{|\vec{\boldsymbol{y}}|^{mn}}$ where…

Following the ideas from a paper by the same author, we prove abstract maximal restriction results for the Fourier transform. Our results deal mainly with maximal operators of convolution-type and $r-$average maximal functions. As a…

We prove a sparse bound for the $m$-sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multisublinear operators are preserved via $\ell^r$-valued…

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.

This paper introduces and studies a class of multilinear fractional bounded mean oscillation operators (denoted {\rm $m$-FBMOOs}) defined on ball-basis measure spaces $(X, \mu, \mathcal{B})$. These operators serve as a generalization of…

In this paper we provide some quantitative mixed-type estimates assuming conditions that imply that $uv\in A_{\infty}$ for Calder\'on-Zygmund operators, rough singular integrals and commutators. The main novelty of this paper lies in the…

We exhibit a range of $\ell ^{p}(\mathbb{Z}^d)$-improving properties for the discrete spherical maximal average in every dimension $d\geq 5$. The strategy used to show these improving properties is then adapted to establish sparse bounds,…

Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{2 \pi i\alpha m^2} f(n - m)}{m}. $$ We prove that, uniformly in $\alpha \in…

We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for…

Let $H_\omega f$ be the Fourier restriction of $f\in L^2(\mathbb{R})$ to an interval $\omega\subset \mathbb{R}$. If $\Omega$ is an arbitrary collection of pairwise disjoint intervals, the square function of $\{H_\omega f: \omega \in…

In this note we give simple proofs of several results involving maximal truncated Calde\'on-Zygmund operators in the general setting of rearrangement invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to…

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…

The regularity of integration kernels forces decay rates of singular values of associated integral operators. This is well-known for symmetric operators with kernels defined on $(a,b) \times (a,b)$, where $(a,b)$ is an interval. Over time,…

In this article, we prove weak type $(1,1)$ bounds for the variation and jump operators corresponding to the family of truncations of singular integrals with rough kernels. This resolves an open question raised by Jones, Seeger and Wright…

For any operator $T$ whose bilinear form can be dominated by a sparse bilinear form, we prove that $T$ is bounded as a map from $L^1(\widetilde{M}w)$ into weak--$L^1(w)$. Our main innovation is that $\widetilde{M}$ is a maximal function…

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 establish a two-weight fractional Poincar\'e-Sobolev sandwich, consisting of a two-weight fractional Poincar\'e-Sobolev inequality and a two-weight embedding from the first-order Sobolev space to a Triebel-Lizorkin space defined via a…

We study sparse domination for operators defined with respect to an atomic filtration on a space equipped with a general measure $\mu$. In the case of Haar shifts, $L^p$-boundedness is known to require a weak regularity condition, which we…

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…