Singular integral operators with operator-valued kernels, and extrapolation of maximal regularity into rearrangement invariant Banach function spaces

摘要

We prove two extrapolation results for singular integral operators with operator-valued kernels, and we apply these results in order to obtain the following extrapolation of L (p) -maximal regularity: if an autonomous Cauchy problem on a Banach space has L (p) -maximal regularity for some , then it has -maximal regularity for every rearrangement invariant Banach function space with Boyd indices and every Muckenhoupt weight . We prove a similar result for nonautonomous Cauchy problems on the line.