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## Banach Center Publications

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## 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 $w\in A_{p_\mathbb E}$.

#### Authors

• Ralph ChillInstitut für Analysis
Fachrichtung Mathematik
TU Dresden
01062 Dresden, Germany
e-mail
• Sebastian KrólFaculty of Mathematics and Computer Science
Nicolaus Copernicus University
ul. Chopina 12/18
87-100 Toruń, Poland
e-mail

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