Bilinear Sobolev-Poincare inequalities and Leibniz-type rules

Frederic Bernicot (1) , Diego Maldonado (2) , Kabe Moen (3) , Virginia Naibo (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Department of Mathematics [Kansas]
3 University of Washington [Seattle]

The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato-Morrey spaces under Sobolev scaling.

Mots clés: Bilinear operators; Poincare inequalities; pseudodifferential operators; fractional Leibniz rules

Domaines: Analyse classique [math.CA]

Frederic Bernicot, Diego Maldonado, Kabe Moen, Virginia Naibo. Bilinear Sobolev-Poincare inequalities and Leibniz-type rules. Journal of Geometric Analysis, 2014, 24, pp.1144-1180. ⟨hal-00587229v4⟩