Integral Operators in Non-Standard Function Spaces: Volume 1

Integral Operators in Non-Standard Function Spaces: Volume 1: Variable Exponent Lebesgue and Amalgam Spaces
Birkhäuser | Mathematics | June 12, 2016 | ISBN-10: 3319210149 | 567 pages | pdf | 6.05 mb

Authors: Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S.

Presents the first comprehensive account of the two-weight theory of basic integral operators, developed in variable exponent Lebesgue spaces
Provides the complete characterizations of Riesz potentials (of functions in variable Lebesgue spaces), weights and space exponents
Explores the weak and strong type estimates criteria for fractional and singular integrals
Introduces new function spaces that unify variable exponent Lebesgue spaces and grand Lebesgue spaces

This book, the result of the authors’ long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them.

The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book’s most distinctive features is that the majority of the statements proved here are in the form of criteria.

The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Topics

Operator Theory

Functional Analysis

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Constructing Transnational Political Spaces

Constructing Transnational Political Spaces: The Multifaceted Political Activism of Mexican Migrants
Palgrave Macmillan US | Politics | May 31 2016 | ISBN-10: 1137558539 | 178 pages | pdf | 2.1 mb

Authors: Schütze, Stephanie

This book analyzes Mexican migrant organizations in the US and their political influence in home communities in Mexico. By connecting multifaceted arenas of Mexican migrant’s activism, it traces the construction of transnational political spaces. The author’s ethnographic work in the state of Michoacán and in Chicago shows how these transnational arenas overcome the limits of traditional political spaces – the nation state and the local community – and bring together intertwined facets of ‘the political’. The book examines how actors engage in politics within transnational spaces; it delineates the different trajectories and agendas of male and female, indigenous and non-indigenous migrant activists; it demonstrates how the local and actor-centered levels are linked to the regional or state levels as well as to the federal levels of politics; and finally, it shows how these multifaceted arenas constitute transnational spaces that have implications for politics and society in Mexico and the US alike

Number of Illustrations and Tables

9 illustrations in colour

Topics

Latin American Politics

Political Theory

Migration

Political Sociology

Human Geography

Social Anthropology

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Separably Injective Banach Spaces

Separably Injective Banach Spaces
Springer | Mathematics | April 27, 2016 | ISBN-10: 3319147404 | 217 pages | pdf | 6.25 mb

Authors: Avilés, A., Cabello Sánchez, F., Castillo, J.M.F.C., González, M., Moreno, Y.

This is the first book dedicated to the subject
Most of the material has never appeared in book form before (and all references to external results have been restricted to material which can be found in books)
The exposition is lively and detailed, in contrast to the typical style of mathematical papers
The monograph contains many annotated open problems, alternative routes and suggestions for new lines of research

This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition).

It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.

Topics

Functional Analysis

Operator Theory

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