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

Abstract

In this paper, the multilinear fractional strong maximal operator ${\mathcal{M}}_{\mathcal{R},\alpha }$ associated with rectangles and corresponding multiple weights $A_{(\vec{p},q),\mathcal{R}}$ are introduced. 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 give a new proof for the weighted estimates of multilinear fractional maximal operator ${\mathcal{M}}_{\alpha }$ associated with cubes and multilinear fractional integral operator ${\mathcal{I}}_{\alpha }$, which is quite different and simple from the proof known before.

Corrected some misprints in Lemma 3.1 and Lemmma 3.2

References in corpus (1)

• The multilinear strong maximal function