A Note on Burkholder Integrals (Journal of Mathematical Study, 2018)
In this note, for $k$-quasiconformal mappings of a bounded domain into thecomplex plane, we give an upper bound of Burkholder integral. Moreover, as an applicationwe obtain an upper bound of the $L^p$-integral of $\sqrt{J_f}$ and $|Df|$ for certain $K$-quasiconformal mappings.
Keywords: Quasiconformal mapping; Burkholder function; Morrey's problem.