Bilinear Sobolev-Poincare inequalities and Leibniz-type rules
Frederic Bernicot (LMJL), Diego Maldonado (KSU), Kabe Moen, Virginia, Naibo (KSU)
TL;DR
This paper develops bilinear Sobolev-Poincare inequalities and explores their applications to Leibniz-type rules, connecting bilinear pseudo-differential and potential operators within Sobolev and Campanato-Morrey spaces.
Contribution
It introduces new bilinear Poincare-type estimates and links bilinear operators to Leibniz rules in advanced function spaces.
Findings
Established bilinear Poincare-type inequalities
Connected bilinear pseudo-differential operators to potential operators
Applied results to Leibniz-type rules in Sobolev and Campanato-Morrey spaces
Abstract
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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems