On multilinear fractional strong maximal operator associated with rectangles and multiple weights

• Mingming Cao ^[1] ; Qingying Xue ^[1] ; Kôzô Yabuta ^[2]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
  2. [2] Kwansei Gakuin University

     Kwansei Gakuin University

     Japón

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 2, 2017, págs. 555-572
• Idioma: inglés
• DOI: 10.4171/RMI/949
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, we introduce the multilinear fractional strong maximal operator MR,α and the corresponding multiple weights A(p→,q),R associated with rectangles. Under the dyadic reverse doubling condition, a necessary and sufficient condition for two-weight inequalities is given. As consequences, we first obtain a necessary and sufficient condition for one-weight inequalities. Then, we present a new proof for the weighted estimates of multilinear fractional integral operator and fractional maximal operator associated with cubes, which is quite different from and simpler than the proof that has been presented previously.