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Miklós Schweitzer
1984 Miklós Schweitzer
6
Miklós Schweitzer 1984- Problem 6
Miklós Schweitzer 1984- Problem 6
Source:
September 4, 2016
college contests
Problem Statement
6. For which Lebesgue-measurable subsets
E
E
E
of the real line does a positive constant
c
c
c
exist for which
sup
−
∞
<
t
<
∞
∣
∫
E
e
i
t
x
f
(
x
)
d
x
∣
≤
c
sup
n
=
0
,
±
1
,
…
∣
∫
E
e
i
n
x
f
(
x
)
d
x
∣
\sup_{-\infty < t<\infty} \left | \int_{E} e^{itx} f(x) dx\right | \leq c \sup_{n=0,\pm 1,\dots } \left | \int_{E} e^{inx} f(x) dx\right |
sup
−
∞
<
t
<
∞
∫
E
e
i
t
x
f
(
x
)
d
x
≤
c
sup
n
=
0
,
±
1
,
…
∫
E
e
in
x
f
(
x
)
d
x
for all integrable functions
f
f
f
on
E
E
E
? (M.17) [G. Halász]
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