We investigate the boundedness of multilinear fractional strong maximal operator
associated with rectangles or related to more general basis with multiple weights
.
In the rectangular setting, we first give an end-point estimate of
,
which not only extends the famous linear result of Jessen, Marcinkiewicz and
Zygmund, but also extends the multilinear result of Grafakos, Liu, Pérez and Torres
() to the
case
.
Then, in the one weight case, we give several equivalent characterizations between
and
.
Based on the Carleson embedding theorem regarding dyadic rectangles, we obtain a
multilinear Fefferman–Stein type inequality, which is new even in the linear case.
We present a sufficient condition for the two weighted norm inequality of
and establish
a version of the vector-valued two weighted inequality for the strong maximal operator
when
.
In the general basis setting, we study the properties of the multiple weight
conditions, including the equivalent characterizations and monotonic properties,
which essentially extends previous understanding. Finally, a survey on multiple
strong Muckenhoupt weights is given, which demonstrates the properties of multiple
weights related to rectangles systematically.
PDF Access Denied
We have not been able to recognize your IP address
44.192.38.143
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.