An optimal symbolic calculus on Besov algebras |
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| Authors: | Grard Bourdaud Madani Moussai Winfried Sickel |
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| Institution: | aInstitut de Mathématiques de Jussieu, Projet d'analyse fonctionnelle, Case 186, 4, place Jussieu, 75252 Paris Cedex 05, France;bDepartment of Mathematics, LMPA, University of M'Sila, P.O. Box 166, 28000 M'Sila, Algeria;cMathematisches Institut, FSU Jena, Ernst-Abbe-Platz 1-2, O7743 Jena, Germany |
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| Abstract: | In this paper we consider Besov algebras on  , that is Besov spaces  for s>1/p. For s>1+(1/p), p>4/3, and q p we prove that the above algebras have a maximal symbolic calculus in the following sense: for any function f belonging locally to  and such that f(0)=0, the associated superposition operator Tf(g):=f○g takes  to itself. |
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| Keywords: | Besov spaces Commutative Banach algebra Symbolic calculus Superposition operators |
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