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