10 ε-distorted diffeomorphisms, O(d) and Functions of Bounded Mean Oscillation (BMO)
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 ...
Get Near Extensions and Alignment of Data in R(superscript)n now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
