G.-C. YANG, Y.-X. FU
Copyright © 2013 SciRes. JAMP
. (3.3)
We need to prove that
sup{,1,2:( )0},
kq
k Ff
σω ω
= =≠
Otherwise,
holds for almost everywhere
and thus, associated with Equation (3.2) we ob-
tain that for arbitrary
it hol ds
( )( )
( )( )
12
2
12
22
22 2
12
2
22
22 2
12
2
1
2
1,
2
q
q
E
D fFfd
F fdCM
αα
α
α
αω
ωωω ω
π
ωωω ω
π
=
≥≥
∫
∫
where
and
is some
positive constant independent of
, that is to say,
(3.4)
The above inequality (3.4) implies
,
which contradicts the assumption (3.3). Thus, we have
sup{,1,2:( )0},
kq
k Ff
σω ω
==≠ <∞
which means
is compactly supported in
. Finally, the same technique as the part of the
proof for the necessity yields that
. Thus, the
proof is complete.
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