<s>
Oscillatory	B-Algorithm
integral	I-Algorithm
operators	I-Algorithm
often	O
appear	O
in	O
many	O
fields	O
of	O
mathematics	O
(	O
analysis	O
,	O
partial	O
differential	O
equations	O
,	O
integral	O
geometry	O
,	O
number	O
theory	O
)	O
and	O
in	O
physics	O
.	O
</s>
<s>
Properties	O
of	O
oscillatory	B-Algorithm
integral	I-Algorithm
operators	I-Algorithm
have	O
been	O
studied	O
by	O
Elias	O
Stein	O
and	O
his	O
school	O
.	O
</s>
<s>
The	O
following	O
bound	O
on	O
the	O
L2	O
→	O
L2	O
action	O
of	O
oscillatory	B-Algorithm
integral	I-Algorithm
operators	I-Algorithm
(	O
or	O
L2	O
→	O
L2	O
operator	O
norm	O
)	O
was	O
obtained	O
by	O
Lars	O
Hörmander	O
in	O
his	O
paper	O
on	O
Fourier	O
integral	O
operators	O
:	O
</s>
<s>
If	O
everywhere	O
on	O
the	O
support	O
of	O
a(x,y )	O
,	O
then	O
there	O
is	O
a	O
constant	O
C	O
such	O
that	O
Tλ	O
,	O
which	O
is	O
initially	O
defined	O
on	O
smooth	O
functions	O
,	O
extends	B-Algorithm
to	O
a	O
continuous	O
operator	O
from	O
L2(Rn )	O
to	O
L2(Rn )	O
,	O
with	O
the	O
norm	O
bounded	O
by	O
,	O
for	O
any	O
λ	O
≥	O
1	O
:	O
</s>
