Bilinear Sobolev–Poincaré Inequalities and Leibniz-Type Rules

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...

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Bibliographic Details
Published in:The Journal of geometric analysis 2014-04, Vol.24 (2), p.1144-1180
Main Authors: Bernicot, Frédéric, Maldonado, Diego, Moen, Kabe, Naibo, Virginia
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-012-9367-4