Problem from Analisis 3 exam.

**veljko** · April 11th 2010, 04:08 AM

Could there be function:

$f<img src=$ 0,\infty) \rightarrow C" alt="f

0,\infty) \rightarrow C" /> so true: $\frac{1}{f} \in L^1(0,\infty)$ and $\overline{lim}_{t\rightarrow 0+} \frac{\int_0^t |f(x)|dx}{t^2}$ ?

Do I need to use some of inequalities or in any other way?

Thank you.

**Drexel28** · April 12th 2010, 02:58 PM

Originally Posted by veljko

Could there be function:

$f<img src=$ 0,\infty) \rightarrow C" alt="f

0,\infty) \rightarrow C" /> so true: $\frac{1}{f} \in L^1(0,\infty)$ and $\overline{lim}_{t\rightarrow 0+} \frac{\int_0^t |f(x)|dx}{t^2}$ ?

Do I need to use some of inequalities or in any other way?

Thank you.

You have likely gotten no responses since this is incomprehensible. Try rewriting it. What is $L^1(0,\infty)$ Do you mean the space with the $\ell_1$ norm $\|(x_1,\cdots,x_n)\|=\sum_{j=1}^{n}|x_j|$ ?

**veljko** · April 12th 2010, 09:21 PM

Update:

Is there a function:

$f<img src=$ 0,\infty) \rightarrow C" alt="f

0,\infty) \rightarrow C" /> so true: $\frac{1}{f} \in L^1(0,\infty)$ and $\overline{lim}_{t\rightarrow 0+} \frac{\int_0^t |f(x)|dx}{t^2} < \infty$ ?

p.s.

$= \{f: \int_{(0,\infty)}|f|dx < + \infty \}$

**maddas** · April 13th 2010, 05:41 AM

edit:nevermind.
edit2: there's probably a one-liner involving maximal functions.

**Jose27** · April 13th 2010, 07:02 AM

Originally Posted by veljko

Update:

Is there a function:

$f<img src=$ 0,\infty) \rightarrow C" alt="f

0,\infty) \rightarrow C" /> so true: $\frac{1}{f} \in L^1(0,\infty)$ and $\overline{lim}_{t\rightarrow 0+} \frac{\int_0^t |f(x)|dx}{t^2} < \infty$ ?

p.s.

$= \{f: \int_{(0,\infty)}|f|dx < + \infty \}$

How about $f(t)=e^t$ .

**maddas** · April 13th 2010, 07:29 AM

Doesn't $\frac1{t^2}\int_0^te^x = \frac{e^t-1}{t^2}$ which goes to infinity?....

Thread: Problem from Analisis 3 exam.

LinkBack

Thread Tools

Display

Problem from Analisis 3 exam.

Similar Math Help Forum Discussions

vector problem - exam revision

Rings exam problem

2 problem exam questions

exam problem

Crazy Domain Problem from an AP Exam

Search Tags