Related papers: Characterizations of Dirichlet-type Spaces
The definition of classical holomorphic function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of holomorphic function spaces on the Hartogs…
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…
The Hardy spaces of Dirichlet series denoted by ${\cal H}^p$ ($p\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two…
A new class of metric measure spaces is introduced and studied. This class generalises the well-established doubling metric measure spaces as well as the spaces (R^n,mu) with mu(B(x,r))<Cr^d, in which non-doubling harmonic analysis has…
The process of identifying a Dirichlet-type space $D(\mu)$ for a positive, Borel measure $\mu$, supported on the unit circle $\mathbb T,$ with a de Branges-Rovnyak space was initiated by Sarason. A characterization of the symbol for a de…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained…
We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…
We demonstrate that the set $L^\infty(X, [-1,1])$ of all measurable functions over a Borel measure space $(X, \mathcal B, \mu )$ with values in the unit interval is typically non-polyhedric when interpreted as a subset of a dual space. Our…
The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of…
Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve BMO. This extends the corresponding Euclidean results by…
Harmonically weighted Dirichlet spaces $\mathcal{D}_\mu$ and de Branges_Rovnyak spaces $\mathcal{H}(b)$ are two fundamental structures in analytic function theory exhibiting rich and often complementary properties. The question of when…
The definition of Toeplitz operators in the Bergman space $A^2(D)$ of square integrable analytic functions in the unit disk in the complex plane is extended in such way that it covers many cases where the traditional definition does not…
We use the formalism of the Bergman tau functions to study the geometry of moduli spaces of holomorphic quadratic differentials on complex algebraic curves. We introduce two natural tau functions and interpret them as holomorphic sections…
In this paper we study the Dirichlet problem for fully nonlinear second-order equations on a riemannian manifold. As in a previous paper we define equations via closed subsets of the 2-jet bundle. Basic existence and uniqueness theorems are…
Let $0<p<\infty$ and $\Psi: [0,1) \to (0,\infty)$, and let $\mu$ be a finite positive Borel measure on the unit disc $\mathbb{D}$ of the complex plane. We define the Lebesgue-Zygmund space $L^p_{\mu,\Psi}$ as the space of all measurable…
We consider mixed normed Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper we compare the results available in the…
We develop a geometric framework for generalized Milnor classifying spaces in the setting of diffeological spaces and infinite-dimensional geometry. Starting from Milnor's construction, we introduce spherical and projective models endowed…