Analysis on Function Spaces of Musielak-Orlicz Type by Osvaldo Mendez

Analysis on Function Spaces of Musielak-Orlicz Type by Osvaldo Mendez

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

"The family of Musielak-Orlicz (M-O) spaces mentioned in the title includes not only those of classical Lebesgue and Orlicz type, but also the spaces with variable exponent that have attracted such a great deal of interest in recent yearsAfter a preparatory chapter in which basic facts are established, a detailed study is made of M-O spaces, following which Sobolev spaces based on them are examined. Finally, there is a chapter giving applications, dealing in particular
with the variable exponent p Laplacian.

A particular virtue of the book is that the unified approach adopted to deal with very general circumstances is accomplished by keeping the technicalities firmly subordinate to the main ideas. It is a welcome addition to the number of books dealing with related topics and should be of definite interest to many."

-Professor David Edmunds, University of Sussex

Osvaldo Mendez is an associate professor at University of Texas at El Paso. His areas of research include Harmonic Analysis, Partial Differential Equations and Theory of Function Spaces. Professor Mendez has authored one book and one edited book.

Jan Lang is a professor of mathematics at The Ohio State University. His areas of interest include the Theory of Integral operators, Approximation Theory, Theory of Function spaces and applications to PDEs. He is the author of two books and one edited book.