, We say that A has the maximal L p -regularity Property (see [24]) if there exists a constant C > 0 such that for all f ? L p (0, +?; X)

, T > 0, instead of (0, +?)

A. Property, , vol.39

, Let A be an unbounded operator on a Banach space X and assume that there exists p ? (1, +?) such that A has the maximal L p -regularity Property. Then, A has the maximal L q -regularity

, Let ?A be the infinitesimal generator of an analytic semigroup on an Hilbert space H. Then, A has the maximal L p -regularity Property for all p ? (0, +?)

, Let (?, µ) be a measure space and let ?A be the infinitesimal generator of an analytic semigroup of contractions (T (t)) t?0 on L 2 (?, µ)

, Corollary B.3. Let ? be an open subset of R n and let u ? H 1 (?) (with u real valued). Then, u + := u ? 0 ? H 1 (?) and ?i ?

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