Extrapolation of $L^p$ maximal regularity for second order Cauchy problems
Volume 112 / 2017
Banach Center Publications 112 (2017), 33-52
MSC: 46D05.
DOI: 10.4064/bc112-0-3
Abstract
If the second order problem $\ddot u + B\dot u + Au = f$ has $L^p$-maximal regularity for some $p\in (1,\infty )$, then it has $\mathbb E_w$-maximal regularity for every rearrangement invariant Banach function space $\mathbb E$ with Boyd indices $p_{\mathbb E}, q_{\mathbb E} \in (1, \infty)$ and for every Muckenhoupt weight $w\in A_{p_\mathbb E}$.
