Related papers: Bounds for discrete multilinear spherical maximal …

For all $p>1$ and all centrally symmetric convex bodies $K\subset \mathbb{R}^d$ define $Mf$ as the centered maximal function associated to $K$. We show that when $d=1$ or $d=2$, we have $||Mf||_p\ge (1+\epsilon(p,K))||f||_p$. For $d\ge 3$,…

In this paper, we prove $L^p$ ($p > 1$) dimension free bounds for the centered Hardy-Littlewood maximal function on real or complex hyperbolic spaces.

In this paper, we study the Lp-bondedness of the spherical maximal function associated to the Dunkl operators.

We prove $\ell^p\big(\mathbb Z^d\big)$ bounds, for $p\in(1, \infty)$, of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon type, and their applications to pointwise ergodic theory. Our…

Let $K$ be a standard H\"older continuous Calder\'on--Zygmund kernel on $\mathbb{R}^{\mathbf{d}}$ whose truncations define $L^2$ bounded operators. We show that the maximal operator obtained by modulating $K$ by polynomial phases of a fixed…

We consider certain Littlewood-Paley square functions on $\Bbb R^2$ and prove sharp estimates for them, from which we can deduce $L^p$ boundedness of maximal functions defined by Fourier multipliers of Bochner-Riesz type on $\Bbb R^2$. This…

We prove that for a finite type curve in $\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \to L^{p}_{1/p}$ regularity result for the averaging operators…

We study a.e. convergence on $L^p$, and Lorentz spaces $L^{p,q}$, $p>\tfrac{2d}{d-1}$, for variants of Riesz means at the critical index $d(\tfrac 12-\tfrac 1p)-\tfrac12$. We derive more general results for (quasi-)radial Fourier…

We prove that the class of trilinear multiplier forms with singularity over a one dimensional subspace, including the bilinear Hilbert transform, admit bounded $L^p$-extension to triples of intermediate $\mathrm{UMD}$ spaces. No other…

We obtain sharp bounds for the modulus of continuity of the uncentered maximal function in terms of the modulus of continuity of the given function, via integral formulas. Some of the results deduced from these formulas are the following:…

For a smooth $k$-dimensional submanifold $\Sigma$ of a $d$-dimensional compact Riemannian manifold $M$, we extend the $L^p(\Sigma)$ restriction bounds of Burq-G\'erard-Tzvetkov -- originally proved for individual Laplace--Beltrami…

We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge 4$.

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses…

We prove that the bilinear Hilbert transforms and maximal functions along certain general plane curves are bounded from $L^2(\mathbb{R})\times L^2(\mathbb{R})$ to $L^1(\mathbb{R})$.

Let $M$ be a product of rank-one symmetric spaces of compact type, each of dimension at least $3$. We establish sharp $L^p$ bounds for the restriction of Laplace--Beltrami eigenfunctions on $M$ to arbitrary submanifolds contained in a…

We study maximal functions related to homogeneous polynomial hypersurfaces in $\mathbb{R}^3$. In a sense made precise in this paper, the region of $(p,q)$ for which we obtain $L^p\rightarrow L^q$ boundedness is optimal up to the endpoints…

We study the lacunary analogue of the $\delta$-discretised spherical maximal operators introduced by Hickman and Jan\v{c}ar, for $\delta \in (0, 1/2)$, and establish the boundedness on $L^p$ for all $1 < p < \infty$, along with the endpoint…

Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$,…

This note presents an example of an increasing sequence $(\lambda_l)_{l=1}^\infty$ such that the maximal operators associated to normalized discrete spherical convolution averages \[ \sup_{l\geq…

In this article we investigate $L^p$ boundedness of the spherical maximal operator $\mathfrak{m}^\alpha$ of (complex) order $\alpha$ on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, which was introduced and studied by El Kohen. We…