A multiplier problem for Fourier-Jacobi expansions in a Banach space (Q1210382)

Generalizing a result of W. Trebels from 1973 there is proved a multiplier theorem for Fourier-Jacobi expansions in the space \(\text{lip}(\gamma,p)\) of functions \(f\in L^ p(0,\pi)\) for which the modulus \(\omega(\phi,f)=\sup\{\| T_ \psi f(\theta)- f(\theta)\|_ p: 0\leq\psi\leq\phi\}\) is \(o(\phi^ \gamma)\), \(T_ \phi f\) being a linear integral operator defined by a suitable non- negative, symmetric kernel \(K(\theta,\phi,\psi)\), with \(\gamma p>1\).