Related papers: A Rudin--de Leeuw type theorem for functions with …

We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…

In our previous articles "A local Paley-Wiener theorem for compact symmetric spaces", Adv. Math. 218 (2008), 202--215, and "Fourier series on compact symmetric spaces" (submitted) we studied Fourier series on a compact symmetric space…

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…

In the classical Hardy space theory of square-summable Taylor series in the complex unit disk there is a circle of ideas connecting Szeg\"o's theorem, factorization of positive semi-definite Toeplitz operators, non-extreme points of the…

We prove some sharp Hardy inequalities for domains with a spherical symmetry. In particular, we prove an inequality for domains of the unit $n$-dimensional sphere with a point singularity, and an inequality for functions defined on the…

Given a complete Riemannian manifold satisfying a weighted Poincar\'{e} inequality and having a bounded below Ricci curvature, various vanishing theorems for harmonic functions and harmonic 1-forms have been published. We generalized these…

In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we will obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $\mathcal…

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 Hardy space…

Let $k$ be a finite field, a $p$-adic field or a number field. Let $K$ be a finite extension of the Laurent series field in $m$ variables $k((x_1,...,x_m))$ or, more generally, a finite extension of the field of rational functions…

The main objective of the present paper is to establish a new uncertainty principle (UP) for the two-sided quaternion Fourier transform (QFT). This result is an extension of a result of Benedicks, Amrein and Berthier, which states that a…

We exploit the Galois symmetries of the little disks operads to show that many differentials in the Goodwillie-Weiss spectral sequences approximating the homology and homotopy of knot spaces vanish at a prime $p$. Combined with recent…

We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…

We prove an analogue of Sadullaev's theorem concerning the size of the set where a maximal totally real manifold can meet a pluripolar set. The manifold has to be of class C-1 only. This readily leads to a version of Shcherbina's theorem…

In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$\alpha$-analytic functions. First, by using a new idea, we prove an improved lemma and the coefficient estimates for bounded polyanalytic…

Let $K\subset \mathbb{R}^d$ be a post-critically finite (p.c.f.) self-similar set with Hausdorff dimension $s$, and $\mu$ be a self-similar probability measure supported on $K$. Let $H^{\alpha}_\mu$, $0<\alpha\le s$, be the Hausdorff…

After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifold with a similarity structure is either complete or the…

Let $X$ be a simplicial complex on $n$ vertices without missing faces of dimension larger than $d$. Let $L_{j}$ denote the $j$-Laplacian acting on real $j$-cochains of $X$ and let $\mu_{j}(X)$ denote its minimal eigenvalue. We study the…

Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in ${\mathcal X}$. In this paper, the…

The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose $K$ is a compact set in the complex plane and 0 belongs to the boundary $\partial K$. Let ${\cal A}(K)$ denote the space of all functions $f$ on $K$…

Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal $I$ in $\loneg$, the space of radial integrable functions on $G=SU(1,1)$, so that $I=\loneg$ or $I=\lonez$---the ideal of…