Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier

Abstract

The maximal operator S * for the spherical summation operator (or disc multiplier ) SR associated with the Jacobi transform through the defining relation d , dµ). In particular {SRf (t)}R>0 converges almost everywhere towards f , for f ∈ L p (R+, dµ), whenever 4α+4 2α+3 < p ≤ 2.