Criteria for $C^m$ -approximability by bianalytic functions on plane compact sets

In a recent joint work of the speaker and M. Ya. Mazalov (Russia, Smolensk) criteria for approximability by bianalytic functions in the norms of the $C^m$-spaces (of Whitney's type) on plane compact sets were obtained for $0<m<2$. These results, together with theorems of A. G. O'Farrell–J. Verdera (the cases $m\ge2$) and M. Ya. Mazalov (the case $m=0$), give a complete list of criteria for approximability by bianalytic functions for all $m\ge0$. These conditions were obtained both for individual functions and (as corollaries) for classes of functions in terms of geometric measure theory.