A note on zeros of bounded holomorphic functions in weakly pseudoconvex domains in C2

摘要

Let ? be a bounded, uniformly totally pseudoconvex domainin C2 with the smooth boundary b?. Assuming that ? satisfies the negative?ˉ property. Let M be a positive, finite area divisor of ?. In thispaper, we will prove that: if ? admits a maximal type F and the Ceck ˇcohomology class of the second order vanishes in ?, there is a boundedholomorphic function in ? such that its zero set is M. The proof is basedon the method given by Shaw [27].