Mean Lipschitz spaces and a generalized Hilbert operator

If $\mu$ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu$ be the Hankel matrix $\mathcal H_\mu =(\mu _{n, k})_{n,k\ge 0}$ with entries $\mu _{n, k}=\mu _{n+k}$, where, for $n\,=\,0, 1, 2, \dots$, $\mu_n$ denotes the moment of order $n$ of $\mu$. This matrix induces formally the operator $$\mathcal{H}_\mu (f)(z)= \sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} \mu_{n,k}{a_k}\right)z^n$$ on the space of all analytic functions $f(z)=\sum_{k=0}^\infty a_kz^k$, in the unit disc $\mathbb{D}$. This is a natural generalization of the classical Hilbert operator. In this paper we study the action of the operators $\mathcal H_\mu$ on mean Lipschitz spaces of analytic functions.Comment: 11 pages, 0 figure

A Hankel matrix acting on spaces of analytic functions

If $\mu$ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu$ be the Hankel matrix $\mathcal H_\mu =(\mu _{n, k})_{n,k\ge 0}$ with entries $\mu _{n, k}=\mu _{n+k}$, where, for $n\,=\,0, 1, 2, \dots$, $\mu_n$ denotes the moment of order $n$ of $\mu$. This matrix induces formally the operator $$\mathcal{H}_\mu (f)(z)= \sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} \mu_{n,k}{a_k}\right)z^n$$ on the space of all analytic functions $f(z)=\sum_{k=0}^\infty a_kz^k$, in the unit disc $\mathbb D$. This is a natural generalization of the classical Hilbert operator. In this paper we improve the results obtained in some recent papers concerning the action of the operators $H_\mu$ on Hardy spaces and on M\"obius invariant spaces.Comment: arXiv admin note: text overlap with arXiv:1612.0830

Multipliers and integration operators between conformally invariant spaces

In this paper we are concerned with two classes of conformally invariant spaces of analytic functions in the unit disc \D, the Besov spaces $B^p$ $(1\le p<\infty )$ and the $Q_s$ spaces $(0<s<\infty )$. Our main objective is to characterize for a given pair $(X, Y)$ of spaces in these classes, the space of pointwise multipliers $M(X, Y)$, as well as to study the related questions of obtaining characterizations of those $g$ analytic in \D such that the Volterra operator $T_g$ or the companion operator $I_g$ with symbol $g$ is a bounded operator from $X$ into $Y$.Comment: To appear in Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSA

Picturesque Violence: Tourism, the Film Industry, and the Heritagization of ‘Bandoleros’ in Spain, 1905–1936

This article examines the debates about the Andalusian ‘bandoleros’ (bandits) in the context of early tourism as a state-guided policy in Spain. As we argue, the development of tourism made Spanish intellectuals reconsider the real armed activity in Andalucía as part of Spanish national heritage and a tourist attraction. Consistent with the stereotypical image of Spain coined by the Romantic travelers, such an early heritagization of brigandry reveals the role of the élites in recasting exotic imagery into modern tourism-shaped identities: in the hands of early century writers, bandits were reshaped as part of the ‘modern picturesque’. Furthermore, the role given to brigands in early cinema allows one to see how the early heritage discourse bridged transnational and centralist interests at the expense of the regional ones, thus foreshadowing the debates about hegemony in present-day heritage studies

Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes

Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. This function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continous input variables. When this is not the case, such as when some of the input variables take integer values, one has to introduce extra approximations. A common approach is to round the suggested variable value to the closest integer before doing the evaluation of the objective. We show that this can lead to problems in the optimization process and describe a more principled approach to account for input variables that are integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods on problems involving integer-valued variables.Comment: 7 page

A family of Dirichlet-Morrey spaces

To each weighted Dirichlet space $\mathcal{D}_p$, $0<p<1$, we associate a family of Morrey-type spaces ${\mathcal{D}}_p^{\lambda}$, $0< \lambda < 1$, constructed by imposing growth conditions on the norm of hyperbolic translates of functions. We indicate some of the properties of these spaces, mention the characterization in terms of boundary values, and study integration and multiplication operators on them.Comment: 18 page