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Mathematische Zeitschrift

, Volume 265, Issue 2, pp 365–400 | Cite as

Use of abstract Hardy spaces, real interpolation and applications to bilinear operators

  • Frédéric BernicotEmail author
Article

Abstract

This paper can be considered as the sequel of Bernicot and Zhao (J Func Anal 255:1761–1796, 2008), where the authors have proposed an abstract construction of Hardy spaces H 1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarify the use of Hardy spaces. Then with the help of the bilinear interpolation theory, we then give applications to study bilinear operators on Lebesgue spaces. These ideas permit us to study singular operators with singularities similar to those of bilinear Calderón-Zygmund operators in a far more abstract framework as in the Euclidean case.

Keywords

Hardy spaces Bilinear operators Atomic decomposition Real interpolation 

Mathematics Subject Classification (2000)

42B20 42B25 42B30 46B70 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Université Paris-Sud XIOrsay CedexFrance

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