What is a paraproduct?

Shirani, Mozhdeh

doi:10.22108/msci.2016.7546

What is a paraproduct?

Document Type : Research Paper

Author

Mozhdeh Shirani

University of Isfahan

10.22108/msci.2016.7546

Abstract

The concept of 'Paraproduct' emerged in the development of Paradifferential operators. This theory itself is a pivotal point in the theory of Beyond Pseudodifferential operators, with the Paraproduct expected to possess properties far beyond those of regular multiplication. Since their inception in 1965, Paraproducts have played a central role in the analysis and partial differential equations. These concepts are related to the theory of two-parameter Calderón-Zygmund theory and form the foundation for many other bilinear operators. Notable applications of these concepts include the well-known theorems such as T1 and Tb theorems, boundedness of Calderón commutator, the Hilbert bilinear transform, theories of pointwise multipliers in function spaces, the theory of corrected compressibility.

Keywords

References

[1] J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4), 14 (1981) 209-249.

[2] A. P. Calderón, Commutators of singular integral operators, Proc. Nat. Acad. Sci. USA, 53 (1965) 1092–1099.

[3] R. R. Coifman and Y. Meyer, Au délà des opérateurs pseudo-différentiels, Société Mathématique de France, 57 (1978).