Related papers: A Note on Maximal Averages in the Plane

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions…

We give a proof of the index theorem of lattice Wilson--Dirac operators, which states that the index of a twisted Dirac operator on the standard torus is described in terms of the corresponding lattice Wilson--Dirac operator. Our proof is…

We combine the split torsor method and the hyperbola method for toric varieties to count rational points and Campana points of bounded height on certain subvarieties of toric varieties.

We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de…

We extend P\'olya's indicator diagram theory to encompass entire functions of order at most 1, allowing functions of maximal type. To do so, we introduce an extension of the complex plane in which indicator diagrams may be unbounded or even…

We consider a type of maximal operators associated to moment curves in $\mathbb R^d, d\geq 3.$ We derive $L^p$ mapping properties for these operators. In a special case, the estimate is sharp.

We provide a representation of the $C^*$-algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the…

We prove a function-field analogue of Bourgain's $L^2$ pointwise ergodic theorem. Let $q$ be a power of a prime $p$, let $\mathbb{F}_q[t]$ be the ring of polynomials over the finite field $\mathbb{F}_q$, and let $\mathbb{F}_q[t][u]$ be the…

In this paper we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization…

We introduce the bilinear Nevo-Thangavelu spherical means on the Heisenberg group $\mathbb{H}^n,$ and derive $L^{p_1}(\mathbb{H}^n) \times L^{p_2}(\mathbb{H}^n) \to L^{p}(\mathbb{H}^n)$ estimates for the single-scale bilinear averaging…

We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.

Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous…

If $L$ is a selfdual Lagrangian $L$ on a reflexive phase space $X\times X^*$, then the vector field $x\to \bar\partial L(x):=\{p\in X^*; (p,x)\in \partial L(x,p)\}$ is maximal monotone. Conversely, any maximal monotone operator $T$ on $X$…

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…

We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proof is inspired by ones by Bourgain and Ionescu, is very…

We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whose discrete Laplace operator converges to the…

The paper considers some new properties of the so-called $A$-maximal numerical range of operators, denoted by $W_{\max}^A(\cdot)$, where $A$ is a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Some…

The aim of this article is to establish the $L^p(\mathbb{R}^2)$-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for…

A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results from the theory of \L{}ojasiewicz inequalities to the…

Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$…