Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

Real interpolation for families of Banach spaces (II)

In this paper, we study the dual space and reiteration theorems for the real method of interpolation for infinite families of Banach spaces introduced in [2]. We also give examples of interpolation spaces constructed with this method.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Chemodiversity and molecular plasticity: recognition processes as explored by property spaces.

In the last few years, a need to account for molecular flexibility in drug-design methodologies has emerged, even if the dynamic behavior of molecular properties is seldom made explicit. For a flexible molecule, it is indeed possible to compute different values for a given conformation-dependent property and the ensemble of such values defines a property space that can be used to describe its molecular variability; a most representative case is the lipophilicity space. In this review, a number of applications of lipophilicity space and other property spaces are presented, showing that this concept can be fruitfully exploited: to investigate the constraints exerted by media of different levels of structural organization, to examine processes of molecular recognition and binding at an atomic level, to derive informative descriptors to be included in quantitative structure--activity relationships and to analyze protein simulations extracting the relevant information. Much molecular information is neglected in the descriptors used by medicinal chemists, while the concept of property space can fill this gap by accounting for the often-disregarded dynamic behavior of both small ligands and biomacromolecules. Property space also introduces some innovative concepts such as molecular sensitivity and plasticity, which appear best suited to explore the ability of a molecule to adapt itself to the environment variously modulating its property and conformational profiles. Globally, such concepts can enhance our understanding of biological phenomena providing fruitful descriptors in drug-design and pharmaceutical sciences.

Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.

Hardy’s inequalities for monotone functions on partly ordered measure spaces

We characterize the weighted Hardy inequalities for monotone functions in Rn +. In dimension n = 1, this recovers the standard theory of Bp weights. For n > 1, the result was previously only known for the case p = 1. In fact, our main theorem is proved in the more general setting of partly ordered measure spaces.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended

How diverse is Cologne Carnival? How migrants appropriate popular art spaces

The present article contributes to the ongoing academic debate on migrants' appropriation of artistic and political spaces in Germany. Cologne, one of the largest cities in Germany, is an interesting example of the tension between political discourse centred around multiculturalism and cultural segregation processes. The 'no fool is illegal' carnival organised by asylum seekers shows their capacity to act, as they reinvent an old local tradition by reinterpreting medieval rituals. Today, different groups and associations appropriate this festive art space: migrants, gays and lesbians, feminists and far-left groups either organise their own parties or take part in the official parties and parades as separate groups. As a result, the celebration of diversity figures on the local political agenda and becomes part of the official carnival festivities. This leads to a blurring of boundaries, whereby mainstream popular culture becomes more and more influenced by multicultural elements.

Invisible Environments: Old Age and its spaces

Despite the progressive ageing of a worldwide population, negative attitudes towards old age have proliferated thanks to cultural constructs and myths that, for decades, have presented old age as a synonym of decay, deterioration and loss. Moreover, even though every human being knows he/she will age and that ageing is a process that cannot be stopped, it always seems distant, far off in the future and, therefore, remains invisible. In this paper, I aim to analyse the invisibility of old age and its spaces through two contemporary novels and their ageing females protagonists –Maudie Fowler in Doris Lessing ’s The Diary of a Good Neighbour and Erica March in Rose Tremain ’s The Cupboard. Although invisible to the rest of society, these elderly characters succeed in becoming significant in the lives of younger protagonists who, immersed in their active lives, become aware of the need to enlarge our vision of old age.