The main result of this paper is
that weak type multiplier theorems for Jacobi expansions yield weak type multiplier
theorems for Hankel transforms.
In recent papers the authors studied multiplier theorems for ultraspherical and
Jacobi expansions. An interesting paper of Igari suggested a new approach to
multiplier theorems that used asymptotics instead of the elaborate machinery used
earlier.
This paper extends the method of Igari to give the first weak type multiplier
theorem for Hankel transforms. This extension is important in itself and because
this method together with the authors’ results for Jacobi multipliers will
generalize to the “radial” functions associated with the other compact symmetric
spaces.
