, Volume 24, Issue 2, pp 1144-1180

Bilinear Sobolev–Poincaré Inequalities and Leibniz-Type Rules

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Abstract

The dual purpose of this article is to establish bilinear Poincaré-type estimates associated with 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.

Communicated by Loukas Grafakos.
F. Bernicot is supported by the ANR under the project AFoMEN no. 2011-JS01-001-01. D. Maldonado, K. Moen and V. Naibo supported by the NSF under grants DMS 0901587, DMS 1201504, and DMS 1101327, respectively.