Course on Function Spaces I

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.

• 1 Introduction.- 2 Preliminaries I – Calculus and measure theory.- 3 Preliminaries II – Functional analysis.- 4 Spaces of continuous functions.- 5 Lᵖ-spaces.- 6 Basics from real and harmonic analysis.