MPEJ Volume 13, No. 6, 20 pp. Received: Nov 29, 2005. Revised: Dec 6, 2006. Accepted: Oct 14, 2007. M. Nicol and A. T\"{o}r\"{o}k Whitney regularity for solutions to the coboundary equation on Cantor sets ABSTRACT: We prove Whitney regularity results for the solutions of the coboundary equation over dynamically defined Cantor sets satisfying a natural geometric regularity condition, in particular hyperbolic basic sets in dimension two. To do this we prove an analogue of Journ\'e's well-known result in the context of Cantor sets satisfying geometric regularity conditions. http://www.maia.ub.es/mpej/Vol/13/6.ps http://www.maia.ub.es/mpej/Vol/13/6.pdf http://www.ma.utexas.edu/mpej/Vol/13/6.ps http://www.ma.utexas.edu/mpej/Vol/13/6.pdf http://mpej.unige.ch/mpej/Vol/13/6.ps http://mpej.unige.ch/mpej/Vol/13/6.pdf