<s>
The	O
Bochner	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
mean	I-Algorithm
is	O
a	O
summability	B-Algorithm
method	I-Algorithm
often	O
used	O
in	O
harmonic	O
analysis	O
when	O
considering	O
convergence	O
of	O
Fourier	O
series	O
and	O
Fourier	O
integrals	O
.	O
</s>
<s>
For	O
and	O
,	O
and	O
may	O
be	O
written	O
as	O
convolution	B-Language
operators	O
,	O
where	O
the	O
convolution	B-Language
kernel	O
is	O
an	O
approximate	B-Algorithm
identity	I-Algorithm
.	O
</s>
<s>
As	O
such	O
,	O
in	O
these	O
cases	O
,	O
considering	O
the	O
almost	O
everywhere	O
convergence	O
of	O
Bochner	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
means	I-Algorithm
for	O
functions	O
in	O
spaces	O
is	O
much	O
simpler	O
than	O
the	O
problem	O
of	O
"	O
regular	O
"	O
almost	O
everywhere	O
convergence	O
of	O
Fourier	O
series/integrals	O
(	O
corresponding	O
to	O
)	O
.	O
</s>
<s>
Another	O
question	O
is	O
that	O
of	O
for	O
which	O
and	O
which	O
the	O
Bochner	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
means	I-Algorithm
of	O
an	O
function	O
converge	O
in	O
norm	O
.	O
</s>
<s>
The	O
case	O
of	O
is	O
not	O
interesting	O
here	O
as	O
convergence	O
follows	O
for	O
in	O
the	O
most	O
difficult	O
case	O
as	O
a	O
consequence	O
of	O
the	O
boundedness	O
of	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
and	O
an	O
argument	O
of	O
Marcel	O
Riesz	O
.	O
</s>
