This book may be considered as the continuation of the monographs
[Tri?]and [Tri?] with the same title. It deals with the theory of
function spaces of type s s B and F as it stands at the beginning of
this century. These two scales of pq pq
spacescovermanywell-knownspacesoffunctionsanddistributionssuchasH]
older- Zygmundspaces, (fractionalandclassical)Sobolevspaces,
BesovspacesandHardy spaces. On the one hand this book is essentially
self-contained. On the other hand we concentrate principally on those
developments in recent times which are related to the nowadays numerous
applications of function spaces to some neighboring areas such as
numerics, signal processing and fractal analysis, to mention only a few
of them. Chapter 1 in [Tri?] is a self-contained historically-oriented
survey of the function spaces considered and their roots up to the
beginning of the 1990s entitled How to measure smoothness. Chapter 1 of
the present book has the same heading indicating continuity. As far as
the history is concerned we will now be very brief, restricting
ourselves to the essentials needed to make this book self-contained and
readable. We complement [Tri?], Chapter 1, by a few points omitted
there. But otherwise we jump to the 1990s, describing more recent
developments. Some of them will be treated later on in detail.