ABSTRACT

In this section we use some of the differential inequalities of Section 4.1 to

obtain linear [ simple and double ] integral operators that preserve bounded

functions. Some of the techniques will be similar to those of the previous

section which dealt with preserving functions with positve real part. However, many of the results will involve sharp bouunds. More precisely,

the problem is : given an integral operator I defined on a class _}( c .J.I,

(4.3-2)

F(z) = - 1-J [f(t) + w(t)]<p(t)t y-I dt. z 'Ycj>(z)

Corollary 4.1 b.1 to prove this result. If we let B(z) = cj>(z) f <p(z),