lowast-SDYM fields and heavenly spaces: I. lowast-SDYM equations as an integrable system

It is shown that the self-dual Yang-Mills (SDYM) equations for the lowast-bracket Lie algebra on a heavenly space can be reduced to one equation (the master equation). Two hierarchies of conservation laws for this equation are constructed. Then the twistor transform and a solution to the Riemann-Hilbert problem are given.