  In this paper we have characterized the space of summability kernels for the
case p=1 and p=2. For other values of p we give a necessary condition for a
function $\Lambda$ to be a summability kernel. For the case p=1, we have
studied the properties of measures which are transferred from $M(\mathbb Z)$ to
$M(\mathbb R)$ through summability kernels. Further, we have extended every
$l_p(\mathbb Z)$ sequences to $L^q(\mathbb R)$ multipliers for certain values
of p and q.
