THE CONVERGENCE AND ITS APPLICATIONS OF MARTINGALE TRANSFORMS WITH RESPECT TO COMPLEX MEASURES

We study the martingale transforms with respect to the complex measure dμ = dv, where satisfies the so-called condition b_∞~+ (K) ∩ a_1 (K). A convergence theorem of the transforms is proved, and then, as an application of it, the pointwise convergence of complex measure martingales is discussed in a precise way.