Collectanea mathematica

, Volume 60, Issue 2, pp 213–238

Weighted inequalities for multilinear fractional integral operators

Article

Abstract

A weighted theory for multilinear fractional integral operators and maximal functions is presented. Sufficient conditions for the two weight inequalities of these operators are found, including “power and logarithmic bumps” and anA condition. For one weight inequalities a necessary and sufficient condition is then obtained as a consequence of the two weight inequalities. As an application, Poincaré and Sobolev inequalities adapted to the multilinear setting are presented.

Keywords

Fractional integrals maximal operators weighted norm inequalities multilinear operators 

MSC2000

26D10 42B25 

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Copyright information

© Universitat de Barcelona 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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