Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

Besov spaces and the Laplacian on fractal H-sets

Nesta tese são estudados espaços de Besov de suavidade generalizada em espaços euclidianos, numa classe de fractais designados conjuntos-h e em estruturas abstractas designadas por espaços-h. Foram obtidas caracterizações e propriedades para estes espaços de funções. Em particular, no caso de espaços de Besov em espaços euclidianos, foram obtidas caracterizações por diferenças e por decomposições em átomos não suaves, foi provada uma propriedade de homogeneidade e foram estudados multiplicadores pontuais. Para espaços de Besov em conjuntos-h foi obtida uma caracterização por decomposições em átomos não suaves e foi construído um operador extensão. Com o recurso a cartas, os resultados obtidos para estes espaços de funções em fractais foram aplicados para definir e trabalhar com espaços de Besov de suavidade generalizada em estruturas abstractas. Nesta tese foi também estudado o laplaciano fractal, considerado a actuar em espaços de Besov de suavidade generalizada em domínios que contêm um conjunto-h fractal. Foram obtidos resultados no contexto de teoria espectral para este operador e foi estudado, à custa deste operador, um problema de Dirichlet fractal no contexto de conjuntos-h.

Weighted Inequalities and Lipschitz Spaces

In this thesis I have characterized the trace measures for particular potential spaces of functions defined on R^n, but "mollified" so that the potentials are de facto defined on the upper half-space of R^n. The potential functions are kind Riesz-Bessel. The characterization of trace measures for these spaces is a test condition on elementary sets of the upper half-space. To prove the test condition as sufficient condition for trace measures, I had give an extension to the case of upper half-space of the Muckenhoupt-Wheeden and Wolff inequalities. Finally I characterized the Carleson-trace measures for Besov spaces of discrete martingales. This is a simplified discrete model for harmonic extensions of Lipschitz-Besov spaces.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Learning beyond books : strategies for ambient media to improve libraries and collaboration spaces as interfaces for social learning

With the advent of digital media and online information resources, public libraries as physical destinations for information access are being increasingly challenged. As a response, many libraries follow the trend of removing bookshelves in order to provide more floorspace for social interaction and collaboration. Such spaces follow a Commons 2.0 model: they are designed to support collaborative work and social learning. The acquisition of skills and knowledge is facilitated as a result of being surrounded by and interacting with a community of likeminded others. Based on the results of a case study on a Commons 2.0 library space, this paper describes several issues of collaboration and social learning in public library settings. Acknowledging the significance of the architectural characteristics of the physical space, we discuss opportunities for ambient media to better reflect the social attributes of the library as a place; i.e. amplify the sense of other co-present library visitors and provide opportunities for shared encounters and conversations, which would remain invisible otherwise. We present the design of a user check-in system for improving the library as a physical destination for social learning, sharing, and inspiration for and by the community.

Digital Literacy and the Spaces of Academic Discourse

Digital literacy poses a particular challenge to the research-led university. Although these universities are often at the forefront of introducing digital literacy initiatives—such as e-learning platforms, technological infrastructure, and digital repositories—these applications of digital literacy tend to be more instrumental or functional than critical or creative. Certainly, this clash of cultures between the instrumental/functional and the critical/analytical is at the heart of debates over the uses of digital literacy in higher education. However, this simple equation of political forces with instrumentality and the corresponding equation of the university with a tradition of reflective thought that brings criticism to bear on instrumentality elide the fact that this conflict is more deeply rooted within the academy. This essay argues that, in fact, much of the resistance to critical uses of digital literacy comes from within the institution of the university itself. That is, the university is bound up in a scriptural economy that prioritises the printed word and that reinforces its power by way of a normative, political, and spatialised academic discourse. It is this print-based scriptural economy—in which this essay must acknowledge its own complicity—that a critical approach to digital literacy threatens to disrupt or lay bare.

Urban knowledge and innovation spaces : concepts, conditions, and contexts

Innovation is one of the key determinants of growth in the globalised knowledge economy, and ‘urban knowledge and innovation spaces’ form the spatial foci for sustained innovation. This paper aims to explore concepts, conditions and contexts that substantiate the development of these spaces of innovation. The paper seeks to identify the foundational elements of knowledge- based urban development to outline the concept of urban knowledge and innovation spaces, and justify its meaning, unique characteristics and growing influence in the contemporary cities. It rationalises the relevance of the three underlying conditions—namely policy, place, and people— to better understand their contribution in the development of such spaces. This paper sheds light over the varied contexts shaping each urban knowledge and innovation space uniquely. The paper reveals the interplay between design and policies that is required for the creation of spaces of innovation that are economically strong, socially connected, spatially stimulating, and environmentally sustainable.

"Unruly women and semiotic spaces": Jay Verney's a mortality tale

Written at a time of significant changes for women and for women writers in Queensland, Australia, Jay Verney's A Mortality Tale (1994), privileges women's experiences of place and seeks to redeem the feminine from its entrapment in masculine stories/discourses of self and place. This chapter draws on Julia Kristeva's conceptualisation of the semiotic as a way of reading Verney's witty and reflective re-articulation of phallocentric orderings of spatiality and gender.

Public space design of knowledge and innovation spaces: Learnings from Kelvin Grove Urban Village, Brisbane

The era of knowledge-based urban development has led to an unprecedented increase in mobility of people and the subsequent growth in new typologies of agglomerated enclaves of knowledge such as knowledge and innovation spaces. Within this context, a new role has been assigned to contemporary public spaces to attract and retain the mobile knowledge workforce by creating a sense of place. This paper investigates place making in the globalized knowledge economy, which develops a sense of permanence spatio-temporally to knowledge workers displaying a set of particular characteristics and simultaneously is process-dependent getting developed by the internal and external flows and contributing substantially in the development of the broader context it stands in relation with. The paper reviews the literature and highlights observations from Kelvin Grove Urban Village, located in Australia’s new world city Brisbane, to understand the application of urban design as a vehicle to create and sustain place making in knowledge and innovation spaces. This research seeks to analyze the modified permeable typology of public spaces that makes knowledge and innovation spaces more viable and adaptive as per the changing needs of the contemporary globalized knowledge society.

Place making facilitators of knowledge and innovation spaces: Insights from European best practices

Knowledge economy seeks its nourishment from diversity and dissemination of ideas and creativity of its talent base. This has led to the acknowledgement of place making as a major strategy to attract and retain the knowledge base into the emerging knowledge and innovation spaces. The study seeks to explore the adoption of place making in this context. Literature and practice provide information to understand the evolution of various spatial typologies and the specialised role of place making in such locations. This helps in determining the key facilitators of place making. The paper takes an interdisciplinary approach and develops an integrated conceptual framework considering dimensions and facilitators of place making. Through the lens of the framework, best practices across Europe—i.e., Cambridge Science Park (UK), 22@Barcelona (Spain), Arabianranta (Finland), Strijp-S (Netherlands), and Digital Hub (Ireland)—are scrutinised to highlight various approaches to place making. The findings provide insights and a discussion into the interplay of form, function, image and underlying processes in globally emerging spatial typologies of contemporary knowledge and innovation spaces.

Connections not boundaries: Future learning and physical spaces

In the developed world, we feel the effects of "digital disruption" in our experiences of the spaces of retail, hospitality, entertainment, finance, arts and culture, and even healthcare. This disruption can take many forms: augmentation of physical experience with a digital complement such as the use of a bespoke mobile application to navigate an art museum, ordering food on digital tablets in a restaurant, recording our health data to share with a doctor. We also rate and review our experiences of a wide range of services and share these opinions with diverse others via the social web.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.