### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

### Cite this

^{p}-L

^{q}estimates for parabolic evolution equations.

*Communications in Partial Differential Equations*,

*22*(9-10), 1647-1669.

**Heat kernels and maximal L ^{p}-L^{q} estimates for parabolic evolution equations.** / Hieber, Matthias Georg; Prüss, Jan.

Research output: Contribution to journal › Article

^{p}-L

^{q}estimates for parabolic evolution equations',

*Communications in Partial Differential Equations*, vol. 22, no. 9-10, pp. 1647-1669.

^{p}-L

^{q}estimates for parabolic evolution equations. Communications in Partial Differential Equations. 1997;22(9-10):1647-1669.

}

TY - JOUR

T1 - Heat kernels and maximal Lp-Lq estimates for parabolic evolution equations

AU - Hieber, Matthias Georg

AU - Prüss, Jan

PY - 1997

Y1 - 1997

N2 - Let A be the generator of an analytic semigroup T on L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp - Lq 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).

AB - Let A be the generator of an analytic semigroup T on L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp - Lq 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).

UR - http://www.scopus.com/inward/record.url?scp=0001098734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001098734&partnerID=8YFLogxK

M3 - Article

VL - 22

SP - 1647

EP - 1669

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 9-10

ER -