In the present paper we obtain a multiplier theorem for Fourier-Jacobi expansions in the space lip$(\gamma,p)$, $\gamma p>1$, which extends an earlier result of Trebels .
"A Multiplier Problem for Fourier-Jacobi Expansions in a Banach Space." Tokyo J. Math. 15 (2) 441 - 450, December 1992. https://doi.org/10.3836/tjm/1270129469