Summary: The authors find the spaces of multipliers \((H^{p,q,\alpha},\ell^s)\), except when \(1<p<2\) and \(0<s<p/(p-1)\), and, for certain values of parameters the spaces of multipliers \((H^{p,q,\alpha},H^{u,v,\beta})\), where \(H^{p,q,\alpha}\) denotes the space of analytic functions on the unit disc such that \((1-r)^\alpha M_p(r,f)\in L^q(dr/(1-r))\). In particular, they calculate the multipliers from Bergman and Hardy spaces into Bloch space.