Summability Kernels for $L^p$ Multipliers

Details Summability Kernels for $L^p$ Multipliers Summability Kernels for $L^p$ Multipliers

2002-01-10

arxiv.org/abs/math/0201086v1

Mathematics

Functional Analysis

Scientific paper

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.

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