TUM Library

Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1: A path to Musielak-Orlicz spaces; 1.1 Introduction; 1.2 Banach function spaces; 1.2.1 The associate space; 1.2.2 Absolute continuity of the norm and continuity of the norm; 1.2.3 Convexity, uniform convexity and smoothness of a norm; 1.2.4 Duality mappings and extremal elements; 1.3 Modular spaces; 1.3.1 Modular convergence and norm convergence; 1.3.2 Conjugate modulars and duality; 1.3.3 Modular uniform convexity; 1.4 The lpn sequence spaces and their properties; 1.4.1 Duality

2.6 Uniform convexity of Musielak-Orlicz spaces2.7 Carathéodory functions and Nemytskii operators on Musielak-Orlicz spaces; 2.8 Further properties of variable exponent spaces; 2.8.1 Duality maps on spaces of variable integrability; 2.9 The Matuszewska-Orlicz index of a Musielak-Orlicz space; 2.10 Historical notes; 3: Sobolev spaces of Musielak-Orlicz type; 3.1 Sobolev spaces: definition and basic properties; 3.1.1 Examples; 3.2 Separability; 3.3 Duality of Sobolev spaces of Musielak-Orlicz type; 3.4 Embeddings, compactness, Poincaré-type inequalities; 4: Applications

Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak-Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area

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