B-valued dyadic derivative

Abstract

The principles of the new maximal operator H* we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz Hp,qX[0,1) to the Lorentz Lp,qX[0,1) for 1/2 < p<∞, 0<q⩽∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in LpX norm for 1⩽p<∞ is a consequence of that the family functions Kn(n∈N) is an approximate identity.