Fonctions lipschitziennes et espaces de Sobolev fractionnaires |
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| Institution: | 1. Department of Surgery, Division of Vascular Surgery, University Medical Centre Groningen, University of Groningen, Groningen, the Netherlands;2. Department of Surgery, Division of Trauma Surgery, University Medical Centre Groningen, University of Groningen, Groningen, the Netherlands;3. Department of Surgery, Division of Transplantation Surgery, University Medical Centre Groningen, University of Groningen, Groningen, the Netherlands;1. School of Mathematics and Statistics, Xi''an Jiaotong University, Xi''an, Shaanxi 710049, China;2. Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;3. Department of Mathematics, and School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA;4. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 117583, Singapore;1. USTHB, laboratoire AMNEDP, faculté de mathématiques, B.P. 32, El Alia, Bab Ezzouar, 16111 Alger, Algeria;2. University of Blida 1, Blida, Algeria;3. Laboratory of Pure and Applied Mathematics, University of M''Sila, Algeria |
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| Abstract: | We consider a semigroup of Markovian and symmetric operators to which we associate fractional Sobolev spaces Dαp (0 < α < 1 and 1 < p < ∞) defined as domains of fractional powers (?Ap)α/2, where Ap is the generator of the semigroup in Lp. We show under rather general assumptions that Lipschitz continuous functions operate by composition on Dαp if p ≥ 2. This holds in particular in the case of the Ornstein-Uhlenbeck semigroup on an abstract Wiener space. |
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