Abstract
Let dμ=ϕdν be a complex valued measure where ν is a non-negative measure and ϕ is a complex valued function which satisfiesb p + orb ∞ + ⊂a 1 condition. We prove some basic martingale inequalities such as B-G inequalities, weak (p, p) and strong (p, p) type inequalities for Banach space valued martingale with respect to complex measure μ.
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