A Fourier restriction operator maps a Schwartz function 
on 
to its Fourier transform on a specified surface 
,
 |
Restriction estimates ask for exponents 
for which
 |
where 
is surface measure and 
is independent of 
. Such an estimate permits extension by density to 
when 
. An arbitrary 
Fourier transform need
not have pointwise values on the surface, so this bounded
extension is the meaning of restriction for such data.
The dual estimate is for the Fourier extension operator from 
to 
, where 
and 
. The Fourier
restriction conjecture specifies expected sharp ranges for curved surfaces.
