Multipliers on Vector Valued Bergman Spaces

Abstract Let X be a complex Banach space and let B p ( X ) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence ( T n ) n of bounded operators between two Banach spaces X and Y defines a multiplier between B p ( X ) and B q ( Y ) (resp. B p ( X ) and l q ( Y )) if for any function we have that belongs to B q ( Y ) (resp. ( T n ( x n )) n ∈ l q ( Y )). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y . New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in B p ( X ) are introduced.