The Journal of Geometric Analysis

, Volume 14, Issue 1, pp 19–46

Extrapolation of Weighted norm inequalities for multivariable operators and applications

Article

DOI: 10.1007/BF02921864

Cite this article as:
Grafakos, L. & Martell, J.M. J Geom Anal (2004) 14: 19. doi:10.1007/BF02921864

Abstract

Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version assumes an initial estimate with different weights in each space and implies boundedness on all products of Lebesgue spaces. Another version assumes an initial estimate with the same weight but yields boundedness on a product of Lebesgue spaces whose indices lie on a line. Applications are given in the context of multilinear Calderón-Zygmund operators. Vector-valued inequalities are automatically obtained for them without developing a multilinear Banach-valued theory. A multilinear extension of the Marcinkiewicz and Zygmund theorem on ℓ2-valued extensions of bounded linear operators is also obtained.

Math Subject Classifications

42B99 

Key Words and Phrases

Extrapolation multilinear operators vector-valued inequalities 

Copyright information

© Mathematica Josephina, Inc. 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbia
  2. 2.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain

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