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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