Possible Duplicate:
Proving an interpolation inequality
Let $f \in L^p$ and $f \in L^r$ where $1 \leqslant p \leqslant r$ . Then can we say that $f \in L^q$ if $p \leqslant q \leqslant r$? ($f : \mathbb R^n \to \mathbb R$)
Possible Duplicate:
Proving an interpolation inequality
Let $f \in L^p$ and $f \in L^r$ where $1 \leqslant p \leqslant r$ . Then can we say that $f \in L^q$ if $p \leqslant q \leqslant r$? ($f : \mathbb R^n \to \mathbb R$)
HINT Split the $L^q$ integral over the sets $A$ and $A^C$, where $A = \{x \in \mathbb{R}^n: f(x) \leq 1\}$ argue out why both are finite making use of the fact that $f \in L^p, L^r$.