In 1910, E E Levi had proved that every domain of holomorphy (called a regularity region in the older terminology) with a sufficiently smooth boundary is a pseudoconvex domain. He asked whether the converse was true, namely whether every pseudoconvex domain a domain of holomorphy.
Sa 1910, EE Levi nagkaroon na ang bawat domain ng holomorphy (na tinatawag na kaayusan ng isang rehiyon sa mas lumang mga terminolohiya) na may sapat makinis na hangganan ay isang pseudoconvex domain. He asked kung ang usap ay totoo, namely kung bawat pseudoconvex domain ng isang domain ng holomorphy.