Related papers: On Rubio de Francia's maximal theorem

Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for $n$-point subsets of $\ell_p$, for $p >…

The optimal $L^p \to L^q$ mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the…

Consider the discrete maximal function acting on finitely supported functions on the integers, \[ \mathcal{C}_\Lambda f(n) := \sup_{\lambda \in \Lambda} | \sum_{p \in \pm \mathbb{P}} f(n-p) \log |p| \frac{e^{2\pi i \lambda p}}{p} |,\] where…

We study the $L^p$ mapping properties of the strong spherical maximal function, which is a multiparameter generalisation of Stein's spherical maximal function. We show that this operator is bounded on $L^p$ for $p > 2$ in all dimensions $n…

Let $(a_n)_{n \in \mathbb{N}}$ be a Hadamard lacunary sequence. We give upper bounds for the maximal gap of the set of dilates $\{a_n \alpha\}_{n \leq N}$ modulo 1, in terms of $N$. For any lacunary sequence $(a_n)_{n \in \mathbb{N}}$ we…

We prove local boundedness of local minimizers of scalar integral functionals $\int_\Omega f(x,\nabla u(x))\,dx$, $\Omega\subset\mathbb R^n$ where the integrand satisfies $(p,q)$-growth of the form \begin{equation*} |z|^p\lesssim…

For $p\in (1,+\infty)$ and $b \in (0, +\infty]$ the $p$-torsion function with Robin boundary conditions associated to an arbitrary open set $\Om \subset \R^m$ satisfies formally the equation $-\Delta_p =1$ in $\Om$ and $|\nabla u|^{p-2}…

We explore the boundedness of the Hardy-Littlewood maximal operator $M$ on variable exponent spaces. Our findings demonstrate that the Muckenhoupt condition, in conjunction with Nekvinda's decay condition, implies the boundedness of $M$…

The main result of this paper is, that if we suppose that a function is absolutely continuous and uniformly H\"older continuous and that its finite difference function does not oscillate infinitely often on a bounded interval, then the…

In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a…

We study the regularity properties of the centered fractional maximal function $M_{\beta}$. More precisely, we prove that the map $f \mapsto |\nabla M_\beta f|$ is bounded and continuous from $W^{1,1}(\mathbb{R}^d)$ to $L^q(\mathbb{R}^d)$…

In this article, we characterize the range of $\alpha$ for which the helical maximal function is bounded from $L^p(|x|^\alpha)$ to itself for $3<p<\infty$. Our result is optimal for $4\leq p<\infty,$ except possibly at end-points.

We provide lower $L^q$ and weak $L^p$-bounds for the localized dyadic maximal operator on $R^n$, when the local $L^1$ and the local $L^p$ norm of the function are given. We actually do that in the more general context of homo- geneous…

In this paper, using the method of blow-up analysis, we obtained a Trudinger-Moser inequality involving L p -norm on a closed Riemann surface and proved the existence of an extremal function for the corresponding Trudinger-Moser functional.…

We obtain a sharp $L^2\times L^2 \to L^1$ boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic dilations of a given function, in terms of the $L^q$ integrability of this…

We introduce the centred and the uncentred triangular maximal operators $\mathcal T$ and $\mathcal U$, respectively, on any locally finite tree in which each vertex has at least three neighbours. We prove that both $\mathcal T$ and…

We prove the discrete restriction conjecture holds with no loss when $p>\frac{2d}{d-4}$ and $d\geq 5$. That is, we show optimal $L^p$ bounds for eigenfunctions of the Laplacian on the square torus for large values of $p$. This improves the…

In this note we consider a generalisation to the metric setting of the recent work [Gu-Yung, JFA 281 (2021), 109075]. In particular, we show that under relatively weak conditions on a metric measure space $(X,d,\nu)$, it holds true that \[…

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

In this work, we consider the Cauchy problem for $u' - Au = f$ with $A$ the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of…