Theory of Function Spaces II

Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces.

Theory of Function Spaces II is self-contained, although it may be considered an update of the author's earlier book of the same title.

The book's 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds.

------ Reviews

The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis.

• Zentralblatt MATH

Includes supplementary material: sn.pub/extras

Texte du rabat

s s T h is b o ok de als w ith the the o ry of func tion s p ac e s of t y p e B and F as it s t ands pq pq at the end of the eigh ties. These t w o scales of spaces co v er man y w ell- kno w n s paces of functions a nd distributions suc h as H olde r-Zy gm und s pac e s , Sob ole v s pac e s , fra- tional Sob o lev s paces (prev ious ly a ls o o ft en referred to a s Bes s e l-p o ten tial s paces ), Be s o v s pac e s , i nhom oge ne ous Hardy s p ac e s , s pac e s of BM O-t y p e and l o c al appro - imation s paces whic h are clos ely c onnected with Morrey-Campanato s paces.

Résumé

From the reviews:

"It is the second volume in a ... series of monographs written by Hans Triebel on this topic. ... the author introduces different approaches and explains their historic background and motivation in view of applications in a very clear and comprehensible way. ... can be recommended as a starting point for scientists who begin to work in this area or just as a brief overview to grasp the key ideas of the theory ... ." (Dorothee Haroske, Zentralblatt MATH, Vol. 1235, 2012)

Contenu
How To Measure Smoothness.- The Spaces and :Definit.- Atoms, Oscillations, and Distinguished Representations.- Key Theorems.- Spaces on Domains.- Mapping Properties of Pseudodifferential Operators.- Spaces on Riemannian Manifolds and Lie Groups.