Related papers: Sparse Endpoint Estimates for Bochner-Riesz Multip…

For each $ d \geq 2$, the Hilbert transform with a polynomial oscillation as below satisfies a $ (1, r )$ sparse bound, for all $ r>1$ $$ H _{ \ast } f (x) = \sup _{\epsilon } \Bigl\lvert \int_{|y| > \epsilon} f (x-y) \frac { e ^{2 \pi i y…

In this paper, we study the almost everywhere convergence problem for the Bochner--Riesz means $S_t^\delta f$ for $f\in L^p(\mathbb R^d)$ in the subcritical range \[ 0\le \delta < \delta(d,p):=d\Big(\frac12-\frac1p\Big)-\frac12, \qquad…

We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions $P_0$ and $P_1$, we find a lower bound for the risk of…

Let $\mathfrak{p}_d(q)$ denote the critical exponent of the Riesz projection from $L^q(\mathbb{T}^d)$ to the Hardy space $H^p(\mathbb{T}^d)$, where $\mathbb{T}$ is the unit circle. We present the state-of-the-art on the conjecture that…

We prove an $\LlogL $-type distributional inequality for the commutator of the Bergman projection with a conjugate Bloch symbol function on the unit ball. Such an inequality can be seen as a Bergman version of a result due to C. P\'{e}rez…

$ \renewcommand{\subset}{\subseteq} \newcommand{\N}{\mathbb N} $For $p\in [2,\infty)$ the metric $X_p$ inequality with sharp scaling parameter is proven here to hold true in $L_p$. The geometric consequences of this result include the…

In this paper, we develop a thorough analysis of the boundedness properties of the maximal operator for the Bochner-Riesz means related to the Fourier-Bessel expansions. For this operator, we study weighted and unweighted inequalities in…

We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…

We generalize the idea of a multiplier in two different ways and generalize a recent result of Geiss, Montomery-Smith and Saksman. First of all, we consider multipliers in the form of a vector acting on a scalar function. Using this…

We prove sharp weak type weighted estimates for a class of sparse operators that includes majorants of standard $\alpha$-fractional singular integrals, fractional integral operators, Marcinkiewicz integral operators, and square functions.…

By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier restriction problem and the Bochner--Riesz problem, extending…

The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative…

For the trace of Besov spaces $B^s_{p,q}$ onto a hyperplane, the borderline case with $s=\frac{n}{p}-(n-1)$ and $0<p<1$ is analysed and a new dependence on the sum-exponent $q$ is found. Through examples the restriction operator defined for…

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to…

We establish estimates for the Poisson kernel, the heat kernel, and Bochner--Riesz means defined in terms of $H=-\Delta+V$, where $V$ is a possibly large rough real-valued scalar potential and $H$ can have negative eigenvalues. All results…

In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces,…

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian…

Let $F$ be a number field, $\pi$ either a unitary cuspidal automorphic representation of $\mathrm{GL}(2)/F$ or a unitary Eisenstein series, and $\chi$ a unitary Hecke character of analytic conductor $C(\chi).$ We develop a regularized…

We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipliers based on natural localized $M^{p\to q}$ norms which…