### Abstract

Let A be the generator of an analytic semigroup T on L^{2}(Ω), where Ω is a homogeneous space with doubling property. We prove maximal L^{p} - L^{q} a-priori estimates for the solution of the parabolic evolution equation u′(t) = Au(t) + f(t), u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).

Original language | English |
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Pages (from-to) | 1647-1669 |

Number of pages | 23 |

Journal | Communications in Partial Differential Equations |

Volume | 22 |

Issue number | 9-10 |

Publication status | Published - 1997 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

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## Cite this

Hieber, M. G., & Prüss, J. (1997). Heat kernels and maximal L

^{p}-L^{q}estimates for parabolic evolution equations.*Communications in Partial Differential Equations*,*22*(9-10), 1647-1669.