An extension of Calderon Transfer Principle

Abstract

We first prove that the well known transfer principle of A. P. Calder\'on can be extended to the vector-valued setting and then we apply this extension to vector-valued inequalities for the Hardy-Littlewood maximal function to prove the vector-valued strong type $L^p$ norm inequalities for $1<p<\infty$ and the vector-valued weak type $(1,1)$ inequality for ergodic maximal function.