A Bessel potential space 
, for 
and 
, is the completion
of the Schwartz space with respect to the norm
 |
where 
is the Fourier multiplier with symbol 
when the Fourier
transform uses 
, and 
is the Laplacian. The notation
is also used for this convention. For nonnegative integer 
, it gives the usual Sobolev
space on 
with an equivalent norm. For 
, it is denoted by 
and has the norm
 |
In particular, 
. The choice of a fractional
Sobolev space convention matters for 
.
