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.
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)
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.