(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ok, so we're in R^N, and we're looking at the unit ball. I wanna prove that the function g(x)=log(log(1+1/r)) is in L^N of the unit ball, where r=|x|.

I also want to prove that its partial derivative are there, but like we say here, one cow at a time.

2. Relevant equations

None, really.

3. The attempt at a solution

Well, I don't remember if it's true, but maybe if xf(x) tends to zero when x tends to zero and f>0, then its integral is finite? I could then try and use it on |g|^N...

Any help would be immensly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is log(log(1+1/r)) in L^N(B(0,1))?

**Physics Forums | Science Articles, Homework Help, Discussion**