Abstract
We study the higher integrability of weights satisfying a reverse Hölder inequality
(
⨏
I
u
β
)
1
β
≤
B
(
⨏
I
u
α
)
1
α
{\biggl{(}\fint_{I}u^{\beta}\biggr{)}^{\frac{1}{\beta}}}\leq B{\biggl{(}\fint_{I}u^{\alpha}\biggr{)}^{\frac{1}{\alpha}}}
for some
B
>
1
B>1
and given
α
<
β
\alpha<\beta
, in the limit cases when
α
∈
{
-
∞
,
0
}
\alpha\in\{-\infty,0\}
and/or
β
∈
{
0
,
+
∞
}
\beta\in\{0,+\infty\}
.
The results apply to the Gehring and Muckenhoupt weights and their corresponding limit classes.