Resumen de Weighted inequalities for multilinear fractional integral operators

Kabe Moen

• 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 an $A_\infty$ condition.

  For one weight inequalities a necessary and sufficient condition is then obtained as a consequence of the two weight inequalities. As an application, Poincar\'e and Sobolev inequalities adapted to the multilinear setting are presented.