### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*128*(4), 1047-1053.

**Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations.** / Hieber, Matthias Georg; Monniaux, Sylvie.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 128, no. 4, pp. 1047-1053.

}

TY - JOUR

T1 - Pseudo-differential operators and maximal regularity results for non-autonomous parabolic equations

AU - Hieber, Matthias Georg

AU - Monniaux, Sylvie

PY - 2000

Y1 - 2000

N2 - 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 L2(ℝ, H). By showing that maximal Lp-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 Lp([0, T], H)-regularity result for solutions of the above equation.

AB - 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 L2(ℝ, H). By showing that maximal Lp-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 Lp([0, T], H)-regularity result for solutions of the above equation.

UR - http://www.scopus.com/inward/record.url?scp=23044520222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044520222&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044520222

VL - 128

SP - 1047

EP - 1053

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -