Bounded Variation and Around

The aim of this monograph is to give a thorough and self-contained account
of functions of (generalized) bounded variation, the methods connected
with their study, their relations to other important function classes,
and their applications to various problems arising in Fourier analysis
and nonlinear analysis.

In the first part the basic facts about spaces of functions of bounded
variation and related spaces are collected, the main ideas which have
been shown to be useful in studying their properties are presented, and
a comparison of their importance and suitability for applications are
provided. The second part is concerned with (sometimes quite surprising
and pathological) properties of nonlinear composition and superposition
operators in such spaces. Finally, relations with Riemann-Stieltjes
integrals and applications to nonlinear integral equations and boundary
value problems are discussed.

The only prerequisite for understanding this book is a modest background
in real analysis, functional analysis, and operator theory. It is addressed
to non-specialists who want to get an idea of the development of the
theory and its applications in the last decades, as well as a glimpse of
the diversity of the directions in which current research is moving.
Since we try to take into account also recent results and state several
open problems, this book might also be a fruitful source of inspiration
for further research.