Analysis on Function Spaces of Musielak-Orlicz Type

Osvaldo Mendez, Jan Lang

• Publisher: Chapman and Hall/CRC
• Year: 2019
• Print ISBN: 9781498762601
• eBook ISBN: 9780429537578
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

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

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• 1 A path to Musielak-Orlicz spaces
• 2 Musielak-Orlicz spaces
• 3 Sobolev spaces of Musielak-Orlicz type
• 4 Applications
• Bibliography
• Author index
• Subject index
• Notation index