10 2. QUASICONFORMAL MAPPING S
2.2. Let /i be a measurable function in a domain ft c C and suppose
||/i||oo 1- 77&en £/iere is a quasiconformal mapping g : Q — C whose complex Bel-
trami coefficient is equal to fi almost everywhere. Moreover every WZo'c (fi) solution
f to the Beltrami equation is of the form
f(z) = F(g(z))
where F : g(Q.) — C is a holomorphic function.
The main results of this paper are sharp generalizations of these two funda-
mental theorems in the degenerate elliptic case. That is when ||/x||oo = 1- This
follows and extends the pioneering work of David . As discussed in the intro-
duction, there is also related earlier work of Lehto on these more general problems,
see [72, 73] where a number of the necessary estimates can be found.
Let us now turn to a more general discussion.