作者:OSCAR BLASCO、PABLO GREGORI
DOI:10.1112/s0024610703004198
日期:2003.6
Given a non-atomic, finite and complete measure space (Omega, Sigma, mu) and a Banach space X, the modulus of continuity for a vector measure F is defined as the function omega(F)(t) = sup(mu(E)less than or equal tot) \F\(E) and the space V-p,V-q(X) of vector measures such that t(-1/p)'omega(F)(t) is an element of L-q((0,mu(Omega)],dt/t) is introduced. It is shown that V-p,V-q(X) contains isometrically L-q,L-p(X) and that L-p,L-q(X) = V-p,V-q(X) if and only if X has the Radon-Nikodym property. It is also proved that Vp,q (X) coincides with the space of cone absolutely summing operators from L-p',L-q' into X and the duality V-p,V-q(X*) = (L-p',L-q'(X))* where 1/p + 1/p' = 1/q + 1/q' = 1. Finally, V-p,V-q(X) is identified with the interpolation space obtained by the real method (V-1(X), V-infinity(X))(1/p)',(q). Spaces where the variation of F is replaced by the semivariation are also considered.