Weighted inequalities for multilinear fractional integral operators

• Autores: Kabe Moen
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 60, Fasc. 2, 2009, págs. 213-238
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.