Related papers: The Geometry of Rough Path Space

The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H^1. We construct spaces through an atomic (or molecular) decomposition. We prove some results about…

Under mild conditions on the space X, we describe the additive structure of the integral cohomology of the space $X^p \times_{C_p}EC_p$ in terms of the cohomology of X. We give weaker results for other similar spaces, and deduce various…

Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case of all positive indices most recent results about these spaces, which include…

We work with non-planar rooted trees which have a label set given by an arbitrary vector space $V$. By equipping $V$ with a complete locally convex topology, we show how a natural topology is induced on the tree algebra over $V$. In this…

Given a smooth hypersurface $X\subset \mathbb{P}^{n+1}$ of degree $d\geqslant 2$, we study the cones $V^h_p\subset \mathbb{P}^{n+1}$ swept out by lines having contact order $h\geqslant 2$ at a point $p\in X$. In particular, we prove that if…

Topological spaces - such as classifying spaces, configuration spaces and spacetimes - often admit extra temporal structure. Qualitative invariants on such directed spaces often are more informative yet more difficult to calculate than…

We show topological genericity for the set of functions in the space X, where X denotes the intersection of the Hardy spaces H^p with p<1, on the open unit disc such that the sequence of Taylor coefficients of the function and of all…

In this paper we obtain the variational characterization of Hardy space $H^p$ for $p\in(\frac n{n+1},1]$ and get estimates for the oscillation operator and the $\lambda$-jump operator associated with approximate identities acting on $H^p$…

For any smooth proper rigid space $X$ over a complete algebraically closed extension $K$ of $\mathbb Q_p$ we give a geometrisation of the $p$-adic Simpson correspondence of rank one in terms of analytic moduli spaces: The $p$-adic character…

In this article, the authors consider the Schr\"{o}dinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative potential…

In this paper, we study the representation of orthogonally additive mappings acting on Hilbert $C^*$-modules and Hilbert $H^*$-modules. One of our main results shows that every continuous orthogonally additive mapping $f$ from a Hilbert…

The set of homogeneous polynomials of degree $D$ is a topological space that contains the subspace $Hyp(D)$ constituted only by hyperbolic polynomials. In 2002, V. I. Arnold conjectured that the number of connected components of $Hyp (D)$…

We provide a theory of manifold-valued rough paths of bounded 3 > p-variation, which we do not assume to be geometric. Rough paths are defined in charts, and coordinate-free (but connection-dependent) definitions of the rough integral of…

Given a pseudoconvex domain D in C^N, N>1, we prove that there is a holomorphic function f on D such that the lengths of paths p: [0,1]--> D along which Re f is bounded above, with p(0) fixed, grow arbitrarily fast as p(1)--> bD. A…

Let $f\colon X\to Y$ be a perfect map between finite-dimensional metrizable spaces and $p\geq 1$. It is shown that the space $C^*(X,\R^p)$ of all bounded maps from $X$ into $\R^p$ with the source limitation topology contains a dense…

We show that a discrete group $\Gamma$ which admits a non-elementary isometric action on a Hadamard manifold of bounded negative curvature admits an isometric action on an $L^p$-space $V$ for some $p>1$ with $H^1(\Gamma,V)\not=0$.

We give an explicit description of the matrix associated to the $U_p$ operator acting on spaces of overconvergent Hilbert modular forms over totally real fields. Using this, we compute slopes for weights in the centre and near the boundary…

In this article we consider rough differential equations (RDEs) driven by non-geometric rough paths, using the concept of branched rough paths introduced in Gubinelli (2004). We first show that branched rough paths can equivalently be…

Given two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces X,Y,Z and…

We investigate the Hardy space H^1_L associated to the Schr\"odinger operator L=-\Delta+V on R^n, where V=\sum_{j=1}^d V_j. We assume that each V_j depends on variables from a linear subspace VV_j of \Rn, dim VV_j \geq 3, and V_j belongs to…