Matts Essén,
Daniel F. Shea,
Charles S. Stanton
(2002)
We give a method for constructing functions and for which has a specified subharmonic minorant . By a theorem of B. Cole,
this procedure establishes integral mean inequalities for conjugate functions. We apply
this method to deduce sharp inequalities for conjugates of functions in the class
, for . In particular, the case yields an improvement of Pichorides’ form of Zygmund’s classical inequality for the
conjugates of functions in . We also apply the method to produce a new...