Related papers: Sparse domination of singular Radon transform

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…

In this paper we analyze the convergence of the following type of series $$ T_N^\alpha f(x,t)=\sum_{j=N_1}^{N_2} v_j(P_{a_{j+1}}^\alpha f(x,t)-P_{a_j}^\alpha f(x,t)),\quad (x,t)\in \mathbb R^{n+1}, \ N=(N_1, N_2)\in \mathbb Z^2,\ \alpha>0,…

We present a fundamentally new proof of the dimensionless Lp boundedness of the Bakry Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion than previous…

We use the thermodynamics of anti-de Sitter gravity to derive sparseness bounds on the spectrum of local operators in holographic conformal field theories. The simplest such bound is $\rho(\Delta) \lesssim…

We consider a positive and power-bounded linear operator $T$ on $L^p$ over a finite measure space and prove that, if $TL^p \subseteq L^q$ for some $q > p$, then the essential spectral radius of $T$ is strictly smaller than $1$. As a special…

In this paper, we analyze the convergence speed of a series related with $\mathcal{P}_\tau^\alpha f$ by discussing the behavior of the family of operators \begin{equation*} T_N^\alpha f(t) = \sum_{j=N_1}^{N_2}…

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to H\"ormander symbol classes $S^m_{\rho,\delta}$ for all…

Operators such as Carleson operator are known to be bounded on $L^p$ for all $1<p<\infty$, but not from $L^1$ to weak-$L^1$ and from $H^p$ to $L^p$ for each $0<p\leq 1$, the object of this article is to give a estimate for all $0<p<\infty$.…

We prove $L^p$ boundedness results, $p > 2$, for local maximal averaging operators over a smooth 2D hypersurface $S$ with either a $C^1$ density function or a density function with a singularity that grows as $|(x,y)|^{-\beta}$ for $\beta <…

Given a curve $\vec{\gamma}=(t^{\alpha_1}, t^{\alpha_2}, t^{\alpha_3})$ with $\vec{\alpha}=(\alpha_1,\alpha_2,\alpha_3)\in \mathbb{R}_{+}^3$, we define the Carleson-Radon transform along $\vec{\gamma}$ by the formula $$…

In graphs and Riemannian manifolds where the kernel of the diffusion semigroup satisfies pointwise sub-Gaussian estimates, we study the range of parameters \( p \in (1, \infty) \) and \( \gamma \in [0, 1] \) for which the quantities \(…

Given a real-analytic function b(x) defined on a neighborhood of the origin with b(0) = 0, we consider local convolutions with kernels which are bounded by |b(x)|^(-a), where a > 0 is the smallest number for which |b(x)|^(-a) is not…

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…

Let $L$ be a one-to-one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the weak Hardy space…

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…

Let $S$ be the dyadic bi-parameter square function $$Sf(x)^{2} = \sum_{R \in \mathcal{D}} |\langle f, h_{R} \rangle|^{2} \frac{1_{R}(x)}{|R|}.$$ We prove that if $T$ is a bi-parameter martingale transform and $f,g$ are suitable test…

Let $p(\cdot):\mathbb R^n\rightarrow(0,\infty)$ be a variable exponent function satisfying the globally log-H\"older continuous condition. In this paper, we obtain the boundedness of para-product operators $\pi_b$ on variable Hardy spaces…

Let $\Gamma$ be a graph endowed with a reversible Markov kernel $p$, and $P$ the associated operator, defined by $Pf(x)=\sum_y p(x,y)f(y)$. Denote by $\nabla$ the discrete gradient. We give necessary and/or sufficient conditions on $\Gamma$…

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…

For appropriate orthonormal wavelet basis $\{\psi_{j\,k}^e \}_{j\in\mathbb{Z}\,k\in\mathbb{Z}^d\,e\in\{0,1\}^d}$, constants $p$ and $\gamma$, if $\mathcal{I}_{\gamma}$ denotes the Riesz fractional integral operator of order $\gamma$ and…