A course on function spaces I Continuous and integrable functions Dominic Breit, Franz Gmeineder

Format:

Book

Author/Creator:

Breit, Dominic, author.

Gmeineder, Franz, 1951- author.

Series:

Universitext

Universitext 2191-6675

Language:

English

Subjects (All):

Function spaces.

Genre:

textbooks.

Textbooks

Textbooks.

Physical Description:

1 online resource

Other Title:

Continuous and integrable functions

Place of Publication:

Cham, Switzerland Springer [2026]

Summary:

"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, 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 analytic properties, weak convergence 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"-- Springer Nature Link

Contents:

Preliminaries I : Calculus and measure theory

Preliminaries II : Functional analysis

Spaces of continuous functions

Lp-spaces

Basics from real and harmonic analysis

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed August 27, 2026)

Other Format:

Print version Breit, Dominic Course on function spaces I

ISBN:

9783030806439

303080643X

OCLC:

1612848223

Access Restriction:

Restricted for use by site license