I just found the following Hölder inequality on a space $\Omega$ with $\lambda(\Omega)=1$ that I don't understand:
It says. Let $(u,v)$ be conjugate exponents, then we get
$$||f||_2 \le ||f||_1^{\frac{1}{2u}} ||f||_{v+1}^{\frac{v+1}{2v}}.$$
Does anybody see what is going on here and how to derive this result?