We study the weighted norm inequality of
-type,
along with its weak-type analogue, for
, where
is an integral operator associated with the nonnegative kernel
on
. Here
denotes the class of positive
Radon measures in
;
, and
.
For both weak-type and strong-type inequalities, we provide conditions which characterize
the measures
for which such an embedding holds. The strong-type
-inequality
for
is closely connected with existence of a positive function
such
that
,
i.e., a supersolution to the integral equation
This study is motivated by solving sublinear equations involving the fractional
Laplacian,
in domains
which have a
positive Green function
for
.
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