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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 …