Regularity of the symbolic calculus in Besov algebras

• Autorzy: Gérard Bourdaud , Massimo Lanza de Cristoforis
• Języki publikacji: EN

Abstrakty

EN

We consider Besov and Lizorkin-Triebel algebras, that is, the real-valued function spaces $B_{p,q}^{s}(ℝⁿ) ∩ L_{∞|(ℝ)$ and ${F_{p,q}^{s}(ℝⁿ)} ∩ L_{∞}(ℝ)$ for all s > 0. To each function f: ℝ → ℝ one can associate the composition operator $T_{f}$ which takes a real-valued function g to the composite function f∘g. We give necessary conditions and sufficient conditions on f for the continuity, local Lipschitz continuity, and differentiability of any order of $T_{f}$ as a map acting in Besov and Lizorkin-Triebel algebras. In some cases, such as for n = 1, such conditions turn out to be necessary and sufficient.

Kategorie tematyczne

• 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 184
• Numer: 3
• Strony: 271-298

Daty

wydano

2008

Twórcy

autor

Gérard Bourdaud

• Institut de Mathématiques de Jussieu, Projet d'analyse fonctionnelle, Case 186, 4 place Jussieu, 75252 Paris Cedex 05, France

autor

Massimo Lanza de Cristoforis

• Dipartimento di Matematica Pura, ed Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy

Identyfikatory

DOI

10.4064/sm184-3-6