Related papers: Carlson's theorem and vertical limit functions

We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional…

We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general…

We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables…

We study the dependence on $\varepsilon$ in the critical dimension $k(n,p,\varepsilon)$ for which one can find random sections of the $\ell_p^n$-ball which are $(1+\varepsilon)$-spherical. We give lower (and upper) estimates for…

For a general $k$-dimensional Brakke flow in $\mathbb{R}^n$ locally close to a $k$-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the…

For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…

For spaces of analytic functions defined on an open set in $\mathbb{C}^n$ that satisfy certain nice properties, we show that operators that preserve shift-cyclic functions are necessarily weighted composition operators. Examples of spaces…

Carlson's theorem estimates the growth of an analytic function along the imaginary axis, provided that the function is zero at non-negative integers. We refine this theorem and describe not only the function's growth but also necessary and…

We establish weak-type $(1,1)$ bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin deterministic sets $B$. As a corollary we obtain the corresponding pointwise convergence result on…

In this article we prove L^p estimates for a general maximal operator, which extend both the classical Coifman-Meyer and Carleson-Hunt theorems in harmonic analysis

The Perron method for solving the Dirichlet problem for $p$-harmonic functions is extended to unbounded open sets in the setting of a complete metric space with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The…

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…

We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for…

We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate, not necessarily symmetric) elliptic operator. First, in…

For $x\in [0,1],$ the run-length function $r_n(x)$ is defined as the length of the longest run of $1$'s amongst the first $n$ dyadic digits in the dyadic expansion of $x.$ Erd\H{o}s and R\'enyi proved that…

In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. We also consider little Hankel operators on these Bergman…

We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…

The almost sure convergence of ergodic averages in Birkhoff's pointwise ergodic theorem is known to fail in the finitely additive setting. We introduce a natural reformulation of almost sure convergence suitable for finitely additive…

Consider a discrete-time martingale, and let $V^2$ be its normalized quadratic variation. As $V^2$ approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian…