Overview
- Provides a thorough introduction to function spaces, from elementary to advanced material
- Carefully guides the reader with explicit learning targets, summaries and numerous exercises
- Includes different approaches and proof strategies
Part of the book series: Universitext (UTX)
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Keywords
- Textbook on function spaces
- Lebesgue spaces
- Hölder spaces
- Lipschitz spaces
- Spaces of test functions
- Schwartz spaces
- Lorentz spaces
- Orlicz spaces
- Fourier transform
- harmonic analysis
About this book
This textbook is the first of a two-part set providing a thorough-yet-accessible introduction to the subject of function spaces. In this first volume, the core topics of spaces of continuous and integrable functions are covered in detail.
Starting from the familiar notions of continuous and smooth functions, the volume gradually progresses to advanced aspects of Lebesgue spaces and their relatives. Key aspects such as basic functional analytics properties, weak convergences and compactness are covered in detail, concluding with an introduction to the fundamentals of real and harmonic analysis. Throughout, the authors provide helpful motivation for the underlying concepts, which they illustrate with selected applications, demonstrating the relevance and practical use of function spaces.
Designed with the student in mind, this self-contained volume offers multiple syllabi, guiding readers from elementary properties to advanced topics. Visual learners will appreciate the inclusion of figures summarising key outcomes, proof strategies, and 'metaprinciples'. Assuming only multivariable calculus and elementary functional analysis, as conveniently summarised in the first chapters, this volume is designed for lecture courses at the graduate level and will also be a valuable companion for young researchers in analysis.
Authors and Affiliations
About the authors
Dominic Breit is Chair of Mathematical Modelling at the Institute of Mathematics of the Clausthal University of Technology. His research interests range from pure topics such as Sobolev spaces, regularity theory for nonlinear PDEs and the calculus of variations, to applications in fluid mechanics.
Franz Gmeineder holds the tenure-track to full professorship 'Theory of PDEs' at the Department of Mathematics and Statistics at the University of Konstanz. His research interests include pure topics from real analysis, function spaces and regularity theory in the calculus of variations, and their interaction in applications.
Bibliographic Information
Book Title: A Course on Function Spaces
Book Subtitle: I: Spaces of continuous and integrable functions
Authors: Dominic Breit, Franz Gmeineder
Series Title: Universitext
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-030-80642-2Due: 12 November 2024
eBook ISBN: 978-3-030-80643-9Due: 12 November 2024
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Illustrations: 23 b/w illustrations, 5 illustrations in colour