An Operator-Valued Transference Principle and Maximal Regularity on Vector-Valued Lp -spaces

A recent vector-valued multiplier theorem for operator-valued Fourier multipliers in L_P (ℝ; X), 1 < p < ∞, X a UMD-space, is combined with the vector-valued transference principle to prove existence of operator-valued R-bounded H ^∞ -functional calculi. These results are applied to maximal L_p -regularity of abstract operator equations as well as to evolutionary integral equations.