Extrapolation of $L^p$ maximal regularity for second order Cauchy problems

Abstract

If the second order problem u'' + Bu' + Au = f has L p-maximal regularity for some p ∈ (1, ∞), then it has E_w-maximal regularity for every rearrangement invariant Banach function space E with Boyd indices p_E, q_E ∈ (1, ∞) and for every Muckenhoupt weight w ∈ A p- .