Theory of Function Spaces

by Hans Triebel

Overview

The book deals with the two scales B^s_p,q and F^s_p,q of spaces of distributions, where ‑∞<s<∞ and 0_n 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.

Product Details

ISBN-13:	9783034604154
Publisher:	Springer Basel
Publication date:	08/20/2010
Series:	Modern Birkhauser Classics Series
Edition description:	1st ed. 1983. 2nd printing 2010
Pages:	281
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

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.

Editorial Reviews

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)

From the Publisher