The 
-dimensional
Riesz transform with respect to a Radon measure 
on 
, for integers 
, is the vector-valued
singular integral with kernel 
. For a bounded,
function 
with compact support, its
hard truncation at radius 
is
 |
Normalization by a dimension-dependent constant is also common. For 
and Lebesgue measure, this gives the classical
Euclidean Riesz transforms up to that normalization. In one dimension the kernel
is 
,
connecting the transform to the Hilbert transform.
For Ahlfors-David regular measures, the David-Semmes problem asks whether a uniform bound
 |
implies uniform rectifiability.
