Boundedness of dyadic derivative and Cesáro mean operator on some B-valued martingale spaces

Abstract

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I * and Cesàro mean operator σ * are bounded from the B-valued martingale Hardy spaces ▪ to Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space.