The Cesàro means of a function 
are the arithmetic means
 |
(1)
|
, 2, ..., where the addend 
is the 
th partial sum
 |
(2)
|
of the Fourier series
 |
(3)
|
for 
. Here, 
is the 
th coefficient
 |
(4)
|
in the Fourier expansion for 
, 
.
Cesàro means are of particular importance in the study of function spaces. For example, a well-known fact is that if 
is in the Lp-space
for 
, the Cesàro means
of 
converge
to 
in the 
-norm and, moreover, if 
is continuous and 
-periodic,
the convergence is uniform.
The 
th Cesàro mean of 
can also be obtained by integrating 
against the 
th Fejér kernel.
