Abstract:
\noindent{\bf Abstract:} Let $f$ be a $K$-quasiconformal mapping in the unit disk $B^2$ of $R^2$.
In this paper, the authors prove
$$\sup_{0<R<1}\int_0^{2\pi}|f(R\e^{i\theta})|^p\mbox{d}\theta<+\infty,$$
for any $ 0<p<\frac1{2K},$ and the supremum $\frac1{2K}$ of $p$ is the best possible.

Key words: Quasiconformal mapping, Hardy space, H\"older inequality