Collectanea mathematica

, Volume 60, Issue 2, pp 213–238

Weighted inequalities for multilinear fractional integral operators

Authors

    • Department of MathematicsUniversity of Kansas
Article

DOI: 10.1007/BF03191210

Cite this article as:
Moen, K. Collect. Math. (2009) 60: 213. doi:10.1007/BF03191210

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 integralsmaximal operatorsweighted norm inequalitiesmultilinear operators

MSC2000

26D1042B25

Copyright information

© Universitat de Barcelona 2009