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

The paper puts forward criteria for approximability by bianalytic functions in the norms of the Whitney-type spaces $C^m$ on planar compact sets with $m \in (0, 2)$. These results, which are analogues of Vitushkin's well-known criteria for uniform rational approximation, together with results of O'Farrell and Verdera (the case $m \geqslant 2$) and Mazalov (the case $m=0$), provide a complete set of criteria for approximability by bianalytic functions for all $m \ge 0$. These conditions for approximability are obtained for both individual functions and (as corollaries) for classes of functions, using the terminology of geometric measure theory.
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