LIPSCHITZ FUNCTIONS AND FRACTIONAL SOBOLEV SPACES

Authors
HIRSCH F
Citation
F. Hirsch, LIPSCHITZ FUNCTIONS AND FRACTIONAL SOBOLEV SPACES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 324(11), 1997, pp. 1227-1230
Citations number
9
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
324
Issue
11
Year of publication
1997
Pages
1227 - 1230
Database
ISI
SICI code
0764-4442(1997)324:11<1227:LFAFSS>2.0.ZU;2-T
Abstract
We consider a semigroup of Markovian and symmetric operators to which we associate fractional Sobolev spaces D-p(alpha) (0 < alpha < 1 and 1 < p < infinity) defined as domains of fractional powers (-A(p))(alpha /2), where A(p) is the generator of the semigroup in L-p. We show unde r rather general assumptions that Lipschitz continuous functions opera te by composition on D-p(alpha) if p greater than or equal to 2. This holds in particular in the case of the Ornstein-Uhlenbeck semigroup on an abstract Wiener space.