### Abstract

In this paper, we show that a pseudo-differential operator associated to a symbol a ε L^{∞}(ℝ × ℝ, L(H)) (H being a Hubert space) which admits a holomorphic extension to a suitable sector of ℂ acts as a bounded operator on L^{2}(ℝ, H). By showing that maximal L^{p}-regularity for the nonautonomous parabolic equation u′(t)+A(t)u(t) = f(t), u(0) = 0 is independent of p ε (1, ∞), we obtain as a consequence a maximal L^{p}([0, T], H)-regularity result for solutions of the above equation.

Original language | English |
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Pages (from-to) | 1047-1053 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 4 |

Publication status | Published - 2000 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Hieber, M. G., & Monniaux, S. (2000). Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations.

*Proceedings of the American Mathematical Society*,*128*(4), 1047-1053.