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2016-2017ÆcSgÆÏ¢C¼êÏ"Áò
July 3§2017
1.0 < α < 1,y²µx
−α
∈ L([0, 1])
2.e1 < p < ∞,y²µf(x) =
sinx
x
∈ L
p
((0, ∞))
f ∈ L
1
((0, ∞))íºf ∈ L
∞
((0, ∞))íº
3.f3RþëY§y²µef r?Û"ÿ8N¤"ÿ8§Kf r?ÛŒÿ
8N¤Œÿ8"
4.f3RþŒ‡§y²µf
0
(x)Œÿ,…ef
0
= 0 a.e.x ∈ R,Kkf 3Rþð
•~ê"
5.f!f
n
´Œÿ8DþA??k•Œÿ¼ê"
£i¤Qãf
n
3Dþ•ÿÝÂñ–f½Â¶
£ii¤y²µef
n
3DþC˜—Âñ–f§Kf
n
3Dþ•ÿÝÂñ–f¶
£iii¤Þ~`²£ii¤¥(؇ƒØ¤á"
6.f ∈ L(R),y²µXJé?¿m8Gkµ
R
G
f(x)dx =
R
G
f(x)dx,Kkµ
f = 0 a.e.x ∈ R
7.f ∈ L(R),y²µ
lim
h→+∞
Z
R
|f(x − h) + f(x)| dx = 2
Z
R
|f(x)| dx
1
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