The Wolff potential probably first appeared in a joint paper between L.I. Hedberg and Th.H. Wolff in 1983 in relation to the spectral synthesis problem for Sobolev spaces. Generally speaking, it is defined for any non-negative Borel measure as follows
where ,
,
, and
is the ball of radius
centered at the point
.
If with
and
, we write
There are several cases
- If
and
, we have
Clearly, this is the well-known Newton potential. Indeed, by exchanging the order of the integral variables, we have