A Course on Function Spaces I

Continuous and Integrable Functions
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.

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 underly