Unconditional martingale difference sequences in Banach spaces

For a Banach space Y  , the question of whether Lp(μ,Y)Lp(μ,Y) has an unconditional basis if 10K>0 so that‖∑i,j∈N(αijyj)di‖Lp(μ,Y)⩽K‖∑i,j∈N‖αijyj‖di‖Lp(μ) holds for every sequence (yj)⊂Y(yj)⊂Y and every choice of finitely supported scalars (αij)(αij).