Theory of Function Spaces

The book deals with the two scales B s p,q and F s p,q of spaces of distributions, where in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart of the book. Chapter 3 deals with corresponding spaces on smooth bounded domains in R n . These results are applied in Chapter 4 in order to study general boundary value problems for regular elliptic differential operators in the above spaces. Shorter Chapters (1 and 5-10) are concerned with: Entire analytic functions, ultra-distributions, weighted spaces, periodic spaces, degenerate elliptic differential equations.

Includes supplementary material: sn.pub/extras

Texte du rabat
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -8n in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart of the book. Chapter 3 deals with corresponding spaces on smooth bounded domains in Rn. These results are applied in Chapter 4 in order to study general boundary value problems for regular elliptic differential operators in the above spaces. Shorter Chapters (1 and 5-10) are concerned with: Entire analytic functions, ultra-distributions, weighted spaces, periodic spaces, degenerate elliptic differential equations.

Résumé

From the reviews:

"There is good reason to think of this book as Volume 1 in a series of (by now) celebrated books on the theory of function spaces treated in a systematic way. It turned out that for many beginners in this part of harmonic analysis this book is still the natural choice to start with. ... this book can still be recommended for people who start their work in function spaces of rather general type and who have some working knowledge in functional analysis ... ." (Dorothee Haroske, Zentralblatt MATH, Vol. 1235, 2012)

Contenu
Spaces of Entire Analytic Functions.- Function Spaces on Rn.- Function Spaces on Domains.- Regular Elliptic Differential Equations.- Homogeneous Function Spaces.- Ultra-Distributions and Weighted Spaces of Entire Analytic Functions.- Weighted Function Spaces on Rn.- Weighted Function Spaces on Domains and Degenerate Elliptic Differential Equations.- Periodic Function Spaces.- Further Types of Function Spaces.