November 2023
Intermediate to advanced
192 pages
3h 29m
English
Up till now, we have spent some time building
-distorted diffeomorphisms from elements of
and Euclidean motions. Here
is small enough. In this chapter, [42], we are going to study the following problem, namely, given a
-distorted diffeomorphism, how well can one approximate it by elements of
? Here
is small enough. We will study this problem in volume measure.
In studying this problem, we find interesting connections of this problem to the space of functions
:
of bounded mean oscillation (BMO) and theJohn–Nirenberg inequality. Here, is as usual a -dimensional volume which in this section we write as ...