Why this question is off-topic?

• Now I want to answer this question myself, at least it covers a large set of functions. – Anixx Mar 5 '14 at 18:23

Let me also agree with Yemon: you need to clarify what you mean by "function", otherwise the question isn't precise. I suppose you mean something like "Lebesgue-integrable function from $\mathbb{R}$ to $\mathbb{R}$", but don't make us guess: tell us!