Meromorphic and Entire Approximation in BMO-Norm Original Research Article

A. Nersesjan and A. Roth proved the local character of the uniform meromorphic approximation on closed sets. In this paper the technique of A. Roth, based on the fusion lemma, is extended to BMO-norm. Thus, by reducing the approximation by meromorphic functions in BMO-norm to rational approximation in this norm on compact sets, the closed sets where the approximation by meromorphic functions is possible are characterized in terms of Hausdorff content. Sufficient conditions for approximation by entire functions are also obtained by using the technique of pushing poles in BMO-norm.