This volume discusses an in-depth theory of function spaces in an
Euclidean setting, including several new features, not previously
covered in the literature. In particular, it develops a unified theory
of anisotropic Besov and Bessel potential spaces on Euclidean corners,
with infinite-dimensional Banach spaces as targets.
It especially highlights the most important subclasses of Besov spaces,
namely Slobodeckii and Hölder spaces. In this case, no restrictions are
imposed on the target spaces, except for reflexivity assumptions in
duality results. In this general setting, the author proves sharp
embedding, interpolation, and trace theorems, point-wise multiplier
results, as well as Gagliardo-Nirenberg estimates and generalizations of
Aubin-Lions compactness theorems.
The results presented pave the way for new applications in situations
where infinite-dimensional target spaces are relevant - in the realm of
stochastic differential equations, for example.