## An Introduction to Sobolev Spaces and Interpolation SpacesAfter publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience. |

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### Contents

II | 1 |

III | 9 |

IV | 15 |

V | 17 |

VI | 21 |

VII | 26 |

VIII | 33 |

IX | 37 |

XXVI | 123 |

XXVII | 127 |

XXVIII | 130 |

XXIX | 137 |

XXX | 141 |

XXXI | 144 |

XXXII | 149 |

XXXIII | 155 |

### Common terms and phrases

American mathematician ball Banach space belongs Besov space BMO(RN bounded open set BV(RN Cc(RN chooses compact support constant continuous functions continuum mechanics converges convolution product decomposition deduces deﬁned Deﬁnition denotes dense derivatives diﬀerent dual Emilio GAGLIARDO equivalent norms exists extends ﬁnd ﬁnite ﬁrst formula Fourier transform France French mathematician G Eq G RN gives Hilbert HS(RN implies integral interpolation spaces Jaak PEETRE Jacques-Louis LIONS Laurent SCHWARTZ Lebesgue measure Lecture Lemma linear continuous form Lipschitz boundary Lipschitz continuous Ll(RN LlONS Lorentz spaces maps mathematical mathematician multi-index nonnegative normed space notices obtained open set Paris partial diﬀerential equations Poincar´e’s Poincare's inequality Proof prove Radon measure reiteration theorem 26.3 result S(RN satisfies scalar Sergei SOBOLEV shows smoothing sequence Sobolev spaces Sobolev's embedding theorem solution space of functions subset subspace Taught on Monday Taught on Wednesday traces University