A Note on Burkholder Integrals

Abstract

In this note, for $k$-quasiconformal mappings of a bounded domain into the complex plane, we give an upper bound of Burkholder integral. Moreover, as an application we obtain an upper bound of the $L^p$-integral of $\sqrt{J_f}$ and $|Df|$ for certain $K$-quasiconformal mappings.