Interpolation subspaces of L^1 of a vector measure and norm inequalities for the integration operator

Calabuig Rodriguez Jose Manuel, Sánchez Pérez Enrique Alfonso, Rodríguez Ruiz José

2012

Contemporary Mathematics

Let m be a Banach space valued measure. We study some domination properties of the integration operator that are equivalent to the existence of Banach ideals of L1(m) that are interpolation spaces. These domination properties are closely connected with some interpolated versions of summing operators, like (p, è)-absolutely continuous operators.