Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Growth and Convergence: The case of China

Growth and Convergence: The Case of China Since the initiation of economic reforms in 1978, China has become one of the world’s fast-growing economies. The rapid growth, however, has not been shared equally across the different regions in China. The prominent feature of substantial differences in incomes and growth rates across the different Chinese regions has attracted the attention of many researchers. This book focuses on issues related to economic growth and convergence across the Chinese regions over the past three decades. The book has eight chapters. Apart from an introduction chapter and a concluding chapter, all the other chapters each deal with some certain aspects of the central issue of regional growth and convergence across China over the past three decades. The whole book is organized as follows. Chapter 1 provides an introduction to the basic issues involved in this book. Chapter 2 tests economic growth and convergence across 31 Chinese provinces during 1981-2005, based on the theoretical framework of the Solow growth model. Chapter 3 investigates the relationship between openness to foreign economic activities, such as foreign trade and foreign direct investment, and the regional economic growth in the case of China during 1981-2005. Chapter 4, based on data of 31 Chinese provinces over the period 1980-2004, presents new evidence on the effects of structural shocks and structural transformation on growth and convergence among the Chinese regions. Chapter 5, by building up an empirical model that takes account of different potential effects of foreign direct investment, focuses on the impacts of foreign direct investment on China’s regional economic performance and growth. Chapter 6 reconsiders the growth and convergence problem of the Chinese regions in an alternative theoretical framework with endogenous saving behavior and capital mobility across regions. Chapter 7, by building up a theoretical model concerning comparative advantage and transaction efficiency, focuses on one of the potential mechanisms through which China achieves its fast economic growth over the past few decades. Chapter 8 concludes the book by summarizing the results from the previous chapters and suggesting directions for further studies.

Producing interactivity : Does media convergence promote interactivity and audience participation?

This study investigates the process of producing interactivity in a converged media environment. The study asks whether more media convergence equals more interactivity. The research object is approached through semi-structured interviews of prominent decision makers within the Finnish media. The main focus of the study are the three big ones of the traditional media, radio, television and the printing press, and their ability to adapt to the changing environment. The study develops theoretical models for the analysis of interactive features and convergence. Case-studies are formed from the interview data and they are evaluated against the models. As a result the cases arc plotted and compared on a four-fold table. The cases are Radio Rock, NRJ, Biu Brother, Television Chat, Olivia and Sanoma News. It is found out that the theoretical models can accurately forecast the results of the case studies. The models are also able to distinguish different aspects of both interactivity and convergence so that a case, which at a first glance seems not to be very interactive is in the end found out to receive second highest scores on the analysis. The highest scores are received by Big Brother and Sanoma News. Through the theory and the analysis of the research data it is found out that the concepts of interactivity and convergence arc intimately intertwined and very hard in many cases to separate from each other. Hence the answer to the main question of this study is yes, convergence does promote interactivity and audience participation. The main theoretical background for the analysis of interactivity follows the work of Came Fleeter, Spiro Kiousis and Sally McMillan. Heeler's six-dimensional definition of interactivity is used as the basis for operationalizing interactivity. The actor-network theory is used as the main theoretical framework to analyze convergence. The definition and operationalization of the actor-network theory into a model of convergence follows the work of Michel Callon. Bruno Latour and especially John Law and Felix Stalder.