Summability Kernels for $L^p$ Multipliers

Abstract

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.