Hermite expansions on R2n for radial functions.

It is proved that the Riesz means SR f, 3 > 0, for the Hermite expansions on Rn', n > 2, satisfy the uniform estimates lISRfllp ? Clf lIp for all radial functions if and only if p lies in the interval 2n/(n + 1 + 2a) < p < 2n/(n 1 26).