Abstract
In this work, we obtain appropriate sharp bounds for a certain class of maximal operators along surfaces of revolution with kernels in
L
q
(
S
n
−
1
)
,
q
>
1
. By using these bounds and using an extrapolation argument, we establish the
L
p
boundedness of the maximal operators when their kernels are in
L
(
log
L
)
α
(
S
n
−
1
)
or in the block space
B
q
0
,
α
−
1
(
S
n
−
1
)
. Our main results represent significant improvements as well as natural extensions of what was known previously.