Vol. 63, No. 1, 1976

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Weak type multipliers for Hankel transforms

William C. Connett, V and Alan Schwartz

Vol. 63 (1976), No. 1, 125–129

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.

Mathematical Subject Classification 2000
Primary: 44A20
Secondary: 42A18
Received: 15 March 1974
Revised: 4 December 1975
Published: 1 March 1976
William C. Connett, V
Alan Schwartz