Via transference principle due to Coifman and Weiss the authors investigate the \(H^\infty\)-calculi for linear operators in vector-valued spaces \(X=L^p(\Omega,\mu,Y)\), \(1<p<\infty\), where \((\Omega,\mu)\) is a measure space and \(Y\) is a Banach space of class \({\mathcal HT}\).