The centered Hardy-Littlewood maximal function averages the absolute value of a locally integrable function
over balls centered at the output point
and takes the supremum over their radii.
For 
on 
,
it is
 |
where 
is the open Euclidean ball and 
is its Lebesgue measure.
The uncentered version instead takes the supremum over
all balls containing 
.
